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Dissertations / Theses on the topic 'Hyperbolic'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Hawksley, Ruth. "Hyperbolic monopoles." Thesis, University of Edinburgh, 1998. http://hdl.handle.net/1842/14019.

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A Euclidean <I>SU</I>(2) monopole consists of a connection and Higgs field on an <I>SU</I>(2) bundle over π<SUP>3</SUP>, satisfying certain partial differential equations. Monopoles may equivalently be described in terms of holomorphic vector bundles on twistor space, algebraic curves in twistor space, rational maps, or solutions to Nahm's equations (a set of ODEs for matrix-valued functions), all satisfying some further conditions. Research by Atiyah, Donaldson, Hitchin, Nahm and others has provided a beautiful and relatively complete picture of these different viewpoints and the links betwee

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2

Lê, Nguyên Khoa 1975. "Time-frequency analyses of the hyperbolic kernel and hyperbolic wavelet." Monash University, Dept. of Electrical and Computer Systems Engineering, 2002. http://arrow.monash.edu.au/hdl/1959.1/8299.

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3

Vlamis, Nicholas George. "Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces." Thesis, Boston College, 2015. http://hdl.handle.net/2345/bc-ir:104137.

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Thesis advisor: Martin J. Bridgeman<br>Thesis advisor: Ian Biringer<br>The first part of this dissertation is on the quasiconformal homogeneity of surfaces. In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for the associated quasiconformal homogeneity constants across all closed hyperbolic surfaces in several cases, including the Torelli group, congruence subgroups, and pure cyclic subgroups. Further, we intro

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4

Ray, Gourab. "Hyperbolic random maps." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/48417.

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Random planar maps have been an object of utmost interest over the last decade and half since the pioneering works of Benjamini and Schramm, Angel and Schramm and Chassaing and Schaeffer. These maps serve as models of random surfaces, the study of which is very important with motivations from physics, combinatorics and random geometry. Uniform infinite planar maps, introduced by Angel and Schramm, which are obtained as local limits of uniform finite maps embedded in the sphere, serve as a very important discrete model of infinite random surfaces. Recently, there has been growing interest to cr

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5

Moussong, Gabor. "Hyperbolic Coxeter groups." Connect to this title online, 1988. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1112044027.

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6

Bult, Fokko Joppe van de. "Hyperbolic hypergeometric functions." [Amsterdam] : Amsterdam : Thomas Stieltjes Institute for Mathematics ; Universiteit van Amsterdam [Host], 2007. http://dare.uva.nl/document/97725.

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7

Koundouros, Stilianos. "Hyperbolic 3-manifolds." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615624.

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8

Markham, Sarah. "Hypercomplex hyperbolic geometry." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/3698/.

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The rank one symmetric spaces of non-compact type are the real, complex, quaternionic and octonionic hyperbolic spaces. Real hyperbolic geometry is widely studied complex hyperbolic geometry less so, whilst quaternionic hyperbolic geometry is still in its infancy. The purpose of this thesis is to investigate the conditions for discrete group action in quaternionic and octonionic hyperbolic 2-spaces and their geometric consequences, in the octonionic case, in terms of lower bounds on the volumes of non-compact manifolds. We will also explore the eigenvalue problem for the 3 x 3 octonionic matri

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9

ALMEIDA, HELLEN ANGELICA DA SILVA. "HYPERBOLIC COXETER GROUPS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2009. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32643@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>Grupos de Coxeter ou de reflexões são importantes no estudo de inúmeras áreas da matemática, incluindo grupos e álgebras de Lie. Nesta dissertação apresentaremos a teoria básica de grupos de reflexões e a classificação dos grupos hiperbólicos, i.e., daqueles que agem no espaço hiperbólico tendo como domínio fundamental um politopo compacto.<br>Groups of Coxeter or of reflections they are important in the study of countl

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10

Marshall, Joseph. "Computation in hyperbolic groups." Thesis, University of Warwick, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369403.

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11

Laibson, David I. "Hyperbolic discounting and consumption." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/11966.

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12

Thompson, James Matthew. "Complex hyperbolic triangle groups." Thesis, Durham University, 2010. http://etheses.dur.ac.uk/478/.

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We prove several discreteness and non-discreteness results about complex hyperbolic triangle groups and discover two new lattices. These results use geometric (explicit construction of a fundamental domain), group theoretic and arithmetic methods.

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13

McLeod, John Angus. "Arithmetic hyperbolic reflection groups." Thesis, Durham University, 2013. http://etheses.dur.ac.uk/7743/.

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This thesis uses Vinberg’s algorithm to study arithmetic hyperbolic reflection groups which are contained in the groups of units of quadratic forms. We study two families of quadratic forms: the diagonal forms −dx_0^2 + x_1^2 + ... + x_n^2 ; and the forms whose automorphism groups contain the Bianchi groups. In the first instance we classify over Q the pairs (d,n) for which such a group can be found, and in some cases we can compute the volumes of the fundamental polytopes. In the second instance we use a combination of the geometric and number theoretic information to classify the reflective

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14

Howard, Tamani M. "Hyperbolic Monge-Ampère Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5322/.

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In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prove some results on the Sobolev gradients that mainly arise from general nonlinear differential equatio

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15

Monaghan, Andrew. "Complex hyperbolic triangle groups." Thesis, University of Liverpool, 2013. http://livrepository.liverpool.ac.uk/14033/.

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In this thesis we study the discreteness criteria for complex hyperbolic triangle groups, generated by reflections in the complex hyperbolic 2-space. A complex hyperbolic triangle group is a group of isometries of the complex hyperbolic plane generated by three complex reflections. We study discreteness of some of these groups using arithmetic and geometric methods. We show that certain complex hyperbolic triangle groups of signature (p,p,2p) and (p,q,pq/(q-p)) are not discrete. The arithmetic methods we use are those studied by Conway and Jones and Parker. We also extend these results further

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16

Bowen, Lewis Phylip. "Density in hyperbolic spaces." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3077409.

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17

Billington, Stephen. "Topics in hyperbolic groups." Thesis, University of Warwick, 1999. http://wrap.warwick.ac.uk/110993/.

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Hyperbolic groups are a class of groups introduced by Gromov in 1987, which form an important part of geometric group theory. In Chapter 1, we give an introduction to this subject. In Chapter 2, we use the theory of complexes of groups to show that the integral homology and cohomology groups of a hyperbolic group are computable by a Turing machine. In Chapter 3, we present the boundary of a hyperbolic group as an inverse limit of topological spaces and use this to give computable estimates for properties of the boundary. In Chapter 4, we investigate symbolic dynamic properties concerning hyper

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18

Dincgez, Umut Can. "Three Dimensional Hyperbolic Grid Generation." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/2/12607147/index.pdf.

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This thesis analyzes procedure of generation of hyperbolic grids formulated by two constraints, which specify grid orthogonality and cell volume. The procedure was applied on a wide range of geometries and high quality two and three dimensional hyperbolic grids were generated by using grid control and smoothing procedures, which supply grid clustering in all directions and prevent grid deformation (grid shock), respectively.

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19

Thomson, Scott Andrew. "Short geodesics in hyperbolic manifolds." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/3604/.

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Given a closed Riemannian n-manifold M, its shortest closed geodesic is called its systole and the length of this geodesic is denoted syst_1(M). For any ε > 0 and any n at least 2 one may construct a closed hyperbolic n-manifold M with syst_1(M) at most equal to ε. Constructions are detailed herein. The volume of M is bounded from below, by A_n/syst_1(M)^(n−2) where A_n is a positive constant depending only on n. There also exist sequences of n-manifolds M_i with syst_1(M_i) → 0 as i → ∞, such that vol(M_i) may be bounded above by a polynomial in 1/syst_1(M_i). When ε is sufficiently small, th

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20

Bowditch, B. H. "Geometrical finiteness for hyperbolic groups." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/99188/.

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In this paper, we describe various definitions of geometrical finiteness for discrete hyperbolic groups in any dimension, and prove their equivalence. This generalises what has been worked out in two and three dimensions by Marden. Beardon, Maskit, Thurston and others. We also discuss the nature of convex fundamental domains for such groups. We begin the paper with a discussion of results related to the Margulls Lemma and Bieberbach Theorems.

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21

Marshall, T. H. (Timothy Hamilton). "Hyperbolic Geometry and Reflection Groups." Thesis, University of Auckland, 1994. http://hdl.handle.net/2292/2140.

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The n-dimensional pseudospheres are the surfaces in Rn+l given by the equations x12+x22+...+xk2-xk+12-...-xn+12=1(1 ≤ k ≤ n+1). The cases k=l, n+1 give, respectively a pair of hyperboloids, and the ordinary n-sphere. In the first chapter we consider the pseudospheres as surfaces h En+1,k, where Em,k=Rk x (iR)m-k, and investigate their geometry in terms of the linear algebra of these spaces. The main objects of investigation are finite sequences of hyperplanes in a pseudosphere. To each such sequence we associate a square symmetric matrix, the Gram matrix, which gives information about angle an

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22

Friel, Karren Janet. "Decision problems in hyperbolic groups." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391970.

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23

Young, R. A. W. "The Uniform Hyperbolic Umbilic Approximation." Thesis, University of Manchester, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376158.

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24

Woodward, J. M. "Integral lattices and hyperbolic manifolds." Thesis, University of York, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441042.

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25

Yaman, Asli. "Boundaries of relatively hyperbolic groups." Thesis, University of Southampton, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432635.

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26

Crampton, Benedict. "Hyperbolic braneworld backgrounds in supergravity." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/27229.

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The manifolds Hp,q [Symbol appears here. To view, please open pdf attachment] are a family of non-compact hyperboloids carrying inhomogeneous Euclidean metrics. In supergravity they appear as an interesting class of dimensional reductions, related to the well known sphere reductions by a simple analytic continuation. The spectrum of lower dimensional modes in these backgrounds is still poorly understood. In this thesis, we construct the complete Pauli reduction of type IIA supergravity on H2,2 [Symbol appears here. To view, please open pdf attachment] . We carefully analyse the spectrum of gra

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27

Alabdullatif, Amal. "Hyperbolic variants of Poncelet's theorem." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/415515/.

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In 1813, J. Poncelet proved his beautiful theorem in projective geometry, Poncelet's Closure Theorem, which states that: if C and D are two smooth conics in general position, and there is an n-gon inscribed in C and circumscribed around D, then for any point of C, there exists an n-gon, also inscribed in C and circumscribed around D, which has this point for one of its vertices. There are some formulae related to Poncelet's Theorem, in which introduce relations between two circles' data (their radii and the distance between their centres), when there is a bicentric n-gon between them. In Eucli

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28

Mondal, Sugata. "Small eigenvalues of hyperbolic surfaces." Toulouse 3, 2013. http://thesesups.ups-tlse.fr/2233/.

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Une surface hyperbolique est une variete complete S de dimension 2 de courbure Sectionnelle egale a -1. Dans cette these on considere l'action du Laplacien de cette metrique. On appelle petite valeur propre toute valeur propre inferieure ou egale a 1/4. Notre theme general de recherche est de borner le nombre de valeurs propres en fonction de la topologie de S lorsque S est d'aire finie. Un theoreme d'Otal-Rosas qui dit que le nombre de petites valeurs propres d'une surface hyperbolique de genre g est au plus 2g-2, confirmant une conjecture de Buser. Nous donnons une version quantitative de ce

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29

Murray, Marilee Anne. "Hyperbolic Geometry and Coxeter Groups." Bowling Green State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1343040882.

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30

Steinberg, Daniel Howard. "Elastic curves in hyperbolic space." Case Western Reserve University School of Graduate Studies / OhioLINK, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=case1058277066.

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31

Walker, Mairi. "Continued fractions and hyperbolic geometry." Thesis, Open University, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.700134.

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This thesis uses hyperbolic geometry to study various classes of both real and complex continued fractions. This intuitive approach gives insight into the theory of continued fractions that is not so easy to obtain from traditional algebraic methods. Using it, we provide a more extensive study of both Rosen continued fractions and even-integer continued fractions than many previous works, yielding new results, and revisiting classical theorems. We also study two types of complex continued fractions, namely Gaussian integer continued fractions and Bianchi continued fractions. As well as providi

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32

Agol, Ian. "Topology of hyperbolic 3-manifolds /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9906477.

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33

Naeve, Trent Phillip. "Conics in the hyperbolic plane." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3075.

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An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.

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34

Heard, Damian. "Computation of hyperbolic structures on 3 dimensional orbifolds /." Connect to theis, 2005. http://eprints.unimelb.edu.au/archive/00001577.

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35

Canadell, Cano Marta. "Computation of Normally Hyperbolic Invariant Manifolds." Doctoral thesis, Universitat de Barcelona, 2014. http://hdl.handle.net/10803/277215.

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The subject of the theory of Dynamical Systems is the evolution of systems with respect to time. Hence, it has many applications to other areas of science, such as Physics, Biology, Economics, etc. and it also has interactions with other parts of Mathematics. The global behavior of a dynamical system is organized by its invariant objects, the simplest ones are equilibria and periodic orbits (and related invariant manifolds). Normally hyperbolic invariant manifolds (NHIM for short) are some of these invariant objects. They have the property to persist under small perturbations of the system.

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36

Leclerc, Marc-Antoine. "The Hyperbolic Formal Affine Demazure Algebra." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35218.

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In this thesis, we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malagón-López, Savage and Zainoulline in two directions. First, we introduce and study the notion of formal Demazure lattices of a Kac-Moody root system and show that the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.

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37

Al-Nayef, Anwar Ali Bayer, and mikewood@deakin edu au. "Semi-hyperbolic mappings in Banach spaces." Deakin University. School of Computing and Mathematics, 1997. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051208.110247.

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The definition of semi-hyperbolic dynamical systems generated by Lipschitz continuous and not necessarily invertible mappings in Banach spaces is presented in this thesis. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces, but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. Bi-shadowing is a combination of the concepts of shadowing and inverse shadowing and is usually used to compare pseudo-trajectories calculated by a computer with the true trajectories. In this thesis, the

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38

Kuhlmann, Sally Malinda. "Geodesic knots in hyperbolic 3 manifolds." Connect to thesis, 2005. http://repository.unimelb.edu.au/10187/916.

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This thesis is an investigation of simple closed geodesics, or geodesic knots, in hyperbolic 3-manifolds.<br>Adams, Hass and Scott have shown that every orientable finite volume hyperbolic 3-manifold contains at least one geodesic knot. The first part of this thesis is devoted to extending this result. We show that all cusped and many closed orientable finite volume hyperbolic 3-manifolds contain infinitely many geodesic knots. This is achieved by studying infinite families of closed geodesics limiting to an infinite length geodesic in the manifold. In the cusped manifold case the limiting g

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39

Bahuaud, Eric. "Intrinsic characterization of asymptotically hyperbolic metrics /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5781.

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40

Hardin, Douglas Patten. "Hyperbolic iterated function systems and applications." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/30864.

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41

Mansouri, Abdol-Reza 1962. "The variational bicomplex for hyperbolic equations /." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33805.

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This thesis presents the geometric investigation of hyperbolic partial differential equations in the plane as carried out by Niky Kamran, Ian Anderson, and Martin Juras. In particular, the relation between the Darboux integrability of an arbitrary hyperbolic equation and the Laplace invariants of the linearization of this equation is established. This extends to non-linear hyperbolic equations in the plane a classical result of Goursat for linear hyperbolic equations. The formal setting for this geometric investigation is afforded by the constrained variational bicomplex, which allows the solu

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42

Cheng, Kan. "Hyperbolic conservation laws with source terms." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343042.

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43

Thorgeirsson, Sverrir. "Hyperbolic geometry: history, models, and axioms." Thesis, Uppsala universitet, Algebra och geometri, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-227503.

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44

Velani, Sanju Lalji. "Metric diophantine approximation in hyperbolic space." Thesis, University of York, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304351.

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45

Bode, Michel. "Random graphs on the hyperbolic plane." Thesis, University of Birmingham, 2016. http://etheses.bham.ac.uk//id/eprint/6526/.

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In this thesis, we study a recently proposed model of random graphs that exhibit properties which are present in a wide range of networks arising in real world settings. The model creates random geometric graphs on the hyperbolic plane, where vertices are connected if they are within a certain threshold distance. We study typical properties of these graphs. We identify two critical values for one of the parameters that act as sharp thresholds. The three resulting intervals of the parameters that correspond to three possible phases of the random structure: A.a.s., the graph is connected; A.a.s.

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46

Cockburn, Alexander Hugh. "Aspects of vortices and hyperbolic monopoles." Thesis, Durham University, 2015. http://etheses.dur.ac.uk/11107/.

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This thesis discusses BPS monopoles in hyperbolic space and BPS vortices in the presence of magnetic impurities. We prove explicit formulae for the spectral curve and rational map of a JNR-type hyperbolic monopole, and we use these to study some Platonic examples as well as some new 1-parameter families analogous to Euclidean monopole scattering. Explicit fields and Braam-Austin data for axial hyperbolic monopoles of a particular mass are derived using a correspondence to 1-monopoles, and this data is deformed to give new 1-parameter families. Numerical techniques are used to study the effect

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47

Braam, Peter J. "Magnetic monopoles and hyperbolic three-manifolds." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:daa73d43-6d58-404c-9926-ebf23f59cfc6.

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Let M = H<sup>3</sup>/Γ be a complete, non-compact, oriented geometrically finite hyperbolic 3-manifold without cusps. By constructing a conformal compactification of M x S<sup>1</sup> we functorially associate to M an oriented, conformally flat, compact 4-manifold X (without boundary) with an S<sup>1</sup>-action. X determines M as a hyperbolic manifold. Using our functor and the differential geometry of conformally flat 4-manifolds we prove that any Γ as above with a limit set of Hausdorff dimension ≤ 1 is Schottky, Fuchsian or extended Fuchsian. Furthermore, the Hodge theory for H<sup>2</su

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48

Saleh, Ibrahim A. "Cluster automorphisms and hyperbolic cluster algebras." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/14195.

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Doctor of Philosophy<br>Department of Mathematics<br>Zongzhu Lin<br>Let A[subscript]n(S) be a coefficient free commutative cluster algebra over a field K. A cluster automorphism is an element of Aut.[subscript]KK(t[subscript]1,[dot, dot, dot],t[subscript]n) which leaves the set of all cluster variables, [chi][subscript]s invariant. In Chapter 2, the group of all such automorphisms is studied in terms of the orbits of the symmetric group action on the set of all seeds of the field K(t[subscript]1,[dot,dot, dot],t[subscript]n). In Chapter 3, we set up for a new class of non-commutative algeb

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49

Schrecker, Matthew. "Hyperbolic problems in fluids and relativity." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:2dec2eb9-4253-4625-a071-0c19d0c1f76d.

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In this thesis, we present a collection of newly obtained results concerning the existence of vanishing viscosity solutions to the one-dimensional compressible Euler equations of gas dynamics, with and without geometric structure. We demonstrate the existence of such vanishing viscosity solutions, which we show to be entropy solutions, to the transonic nozzle problem and spherically symmetric Euler equations in Chapter 4, in both cases under the simple and natural assumption of relative finite-energy. In Chapter 5, we show that the viscous solutions of the one-dimensional compressible Navier-S

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50

De, Capua Antonio. "Hyperbolic volume estimates via train tracks." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:426f7186-e881-482b-90d8-5cbb9b9a38b7.

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In this thesis we describe how to estimate the distance spanned in the pants graph by a train track splitting sequence on a surface, up to multiplicative and additive constants. If some moderate assumptions on a splitting sequence are satisfied, each vertex set of a train track in it will represent a vertex of a graph which is naturally quasi-isometric to the pants graph; moreover the splitting sequence gives an edge-path in this graph so, more precisely, our distance estimate holds between the extreme points of this path. The present distance estimate is inspired by a result of Masur, Mosher

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