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Relevant bibliographies by topics / Hyperbolic space

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Academic literature on the topic 'Hyperbolic space'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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Journal articles on the topic "Hyperbolic space"

1

Levitt, Gilbert, and Harold Rosenberg. "hyperbolic space." Duke Mathematical Journal 52, no. 1 (1985): 53–59. http://dx.doi.org/10.1215/s0012-7094-85-05204-4.

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Babich, M., and A. Bobenko. "hyperbolic space." Duke Mathematical Journal 72, no. 1 (1993): 151–85. http://dx.doi.org/10.1215/s0012-7094-93-07207-9.

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Yegin, R., and U. Dursun. "On Submanifolds of Pseudo-Hyperbolic Space with 1-Type Pseudo-Hyperbolic Gauss Map." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 4 (2016): 315–37. http://dx.doi.org/10.15407/mag12.04.315.

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Xuegang, Yu. "Hyperbolic Hilbert space." Advances in Applied Clifford Algebras 10, no. 1 (2000): 49–60. http://dx.doi.org/10.1007/bf03042009.

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Chen, Chiang-Mei, Pei-Ming Ho, Ishwaree P. Neupane, John E. Wang, and Nobuyoshi Ohta. "Hyperbolic space cosmologies." Journal of High Energy Physics 2003, no. 10 (2003): 058. http://dx.doi.org/10.1088/1126-6708/2003/10/058.

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IZUMIYA, SHYUICHI, DONGHE PEI, and TAKASI SANO. "SINGULARITIES OF HYPERBOLIC GAUSS MAPS." Proceedings of the London Mathematical Society 86, no. 2 (2003): 485–512. http://dx.doi.org/10.1112/s0024611502013850.

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In this paper we adopt the hyperboloid in Minkowski space as the model of hyperbolic space. We define the hyperbolic Gauss map and the hyperbolic Gauss indicatrix of a hypersurface in hyperbolic space. The hyperbolic Gauss map has been introduced by Ch. Epstein [J. Reine Angew. Math. 372 (1986) 96–135] in the Poincaré ball model, which is very useful for the study of constant mean curvature surfaces. However, it is very hard to perform the calculation because it has an intrinsic form. Here, we give an extrinsic definition and we study the singularities. In the study of the singularities of the hyperbolic Gauss map (indicatrix), we find that the hyperbolic Gauss indicatrix is much easier to calculate. We introduce the notion of hyperbolic Gauss–Kronecker curvature whose zero sets correspond to the singular set of the hyperbolic Gauss map (indicatrix). We also develop a local differential geometry of hypersurfaces concerning their contact with hyperhorospheres.2000 Mathematical Subject Classification: 53A25, 53A05, 58C27.

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Dursun, Uğur, and Rüya Yeğin. "Hyperbolic submanifolds with finite type hyperbolic Gauss map." International Journal of Mathematics 26, no. 02 (2015): 1550014. http://dx.doi.org/10.1142/s0129167x15500147.

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We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.

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Blåsjö, Viktor. "Hyperbolic Space for Tourists." Journal of Humanistic Mathematics 3, no. 2 (2013): 77–95. http://dx.doi.org/10.5642/jhummath.201302.06.

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Chaturvedi, S., G. J. Milburn, and Zhongxi Zhang. "Interference in hyperbolic space." Physical Review A 57, no. 3 (1998): 1529–35. http://dx.doi.org/10.1103/physreva.57.1529.

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Bezdek, Károly, Márton Naszódi, and Deborah Oliveros. "Antipodality in hyperbolic space." Journal of Geometry 85, no. 1-2 (2006): 22–31. http://dx.doi.org/10.1007/s00022-006-0038-0.

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Dissertations / Theses on the topic "Hyperbolic space"

1

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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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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Cuschieri, Thomas. "Complete noncompact CMC surfaces in hyperbolic 3-space." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/3135/.

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In this thesis we study the asymptotic Plateau problem for surfaces with constant mean curvature (CMC) in hyperbolic 3-space H3. We give a new, geometrically transparent proof of the existence of a CMC surface spanning any given Jordan curve on the sphere at infinity of H3, for mean curvature lying in the range (-1,1). Our proof does not require methods from geometric measure theory, and yields an immersed disk as solution. We then study the dependence of the solution surface on the boundary data. We view the set of H-surfaces (CMC surfaces with mean curvature equal to H) as consisting of the conformal H-harmonic maps. We therefore begin by showing smooth dependence on boundary data for H-harmonic maps (with |H| < 1) which solve a Dirichlet problem at infinity. This is achieved by showing that the linearised H-harmonic map operator is invertible as a map between appropriate function spaces. Finally we show smooth dependence on boundary data for H-surfaces which lie in a neighbourhood of the totally umbilic spherical caps {H}. This is achieved by studying the mapping properties of the so-called conformality operator. We use methods from complex geometry to show that the linearisation of this operator at a cap H is an isomorphism for all H ∈ (−1, 1).

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Raab, Erik. "Constant mean curvature surfaces in hyperbolic 3-space." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-225923.

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The aim of this bachelor's thesis has been to investigate surfaces that are the main contributions to scattering amplitudes in a type of string theory. These are constant mean curvature surfaces in hyperbolic 3-space. Classically the way to find such surfaces has been to solve a non-linear partial differential equation. In many spaces constant mean curvature surfaces are intimately connected to certain harmonic maps, known as the Gauss maps. In 1995 Dorfmeister, Pedit, and Wu established a method for constructing harmonic maps into so-called symmetric spaces. I investigate a generalization of this method that can be applied to find constant mean curvature surfaces in hyperbolic 3-space by using the intimate connection between these surfaces and harmonic maps. This method relies on a factorization of a Lie-group valued map. I show an explicit method for finding the factorization in terms of what is known as the Birkhoff factorization. Because approximation methods for the Birkhoff factorization are known, this allowed me to use the method constructively to find constant mean curvature surfaces in hyperbolic 3-space.

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Warakkagun, Sangsan. "Connectivity of the space of pointed hyperbolic surfaces:." Thesis, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109215.

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Thesis advisor: Ian Biringer<br>We consider the space $\rootedH2$ of all complete hyperbolic surfaces without boundary with a basepoint equipped with the pointed Gromov-Hausdorff topology. Continuous paths within $\rootedH2$ arising from certain deformations on a hyperbolic surface and concrete geometric constructions are studied. These include changing some Fenchel-Nielsen parameters of a subsurface, pinching a simple closed geodesic to a cusp, and inserting an infinite strip along a proper bi-infinite geodesic. We then use these paths to show that $\rootedH2$ is path-connected and that it is locally weakly connected at points whose underlying surfaces are either the hyperbolic plane or hyperbolic surfaces of the first kind<br>Thesis (PhD) — Boston College, 2021<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Mathematics

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Yu, Hao [Verfasser], and Claus [Akademischer Betreuer] Gerhardt. "Dual flows in hyperbolic space and de Sitter space / Hao Yu ; Betreuer: Claus Gerhardt." Heidelberg : Universitätsbibliothek Heidelberg, 2017. http://d-nb.info/1178010392/34.

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Herold, Felix [Verfasser], and D. [Akademischer Betreuer] Hug. "Random mosaics in hyperbolic space / Felix Herold ; Betreuer: D. Hug." Karlsruhe : KIT-Bibliothek, 2021. http://d-nb.info/1229514767/34.

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Yarmola, Andrew. "Convex hulls in hyperbolic 3-space and generalized orthospectral identities." Thesis, Boston College, 2016. http://hdl.handle.net/2345/bc-ir:106788.

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Thesis advisor: Martin Bridgeman<br>We begin this dissertation by studying the relationship between the Poincaré metric of a simply connected domain Ω ⊂ ℂ and the geometry of Dome(Ω), the boundary of the convex hull of its complement. Sullivan showed that there is a universal constant K[subscript]eq[subscript] such that one may find a conformally natural K[subscript]eq[subscript]-quasiconformal map from Ω to Dome(Ω) which extends to the identity on ∂Ω. Explicit upper and lower bounds on K[subscript]eq[subscript] have been obtained by Epstein, Marden, Markovic and Bishop. We improve upon these upper bounds by showing that one may choose K[subscript]eq[subscript] ≤ 7.1695. As part of this work, we provide stronger criteria for embeddedness of pleated planes. In addition, for Kleinian groups Γ where N = ℍ³/Γ has incompressible boundary, we give improved bounds for the average bending on the convex core of N and the Lipschitz constant for the homotopy inverse of the nearest point retraction. In the second part of this dissertation, we prove an extension of Basmajian's identity to n-Hitchin representations of compact bordered surfaces. For 3-Hitchin representations, we provide a geometric interpretation of this identity analogous to Basmajian's original result. As part of our proof, we demonstrate that for a closed surface, the Lebesgue measure on the Frenet curve of an n-Hitchin representation is zero on the limit set of any incompressible subsurface. This generalizes a classical result in hyperbolic geometry. In our final chapter, we prove the Bridgeman-Kahn identity for all finite volume hyperbolic n-manifolds with totally geodesic boundary. As part of this work, we correct a commonly referenced expression of the volume form on the unit tangent bundle of ℍⁿ in terms of the geodesic end point parametrization<br>Thesis (PhD) — Boston College, 2016<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Mathematics

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Mole, Adam [Verfasser], and Arthur [Akademischer Betreuer] Bartels. "A flow space for a relatively hyperbolic group / Adam Mole ; Betreuer: Arthur Bartels." Münster : Universitäts- und Landesbibliothek Münster, 2013. http://d-nb.info/1141680874/34.

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Tyler, B. M. "A computational method for the construction of Siegel sets in complex hyperbolic space." Thesis, University College London (University of London), 2010. http://discovery.ucl.ac.uk/147750/.

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This thesis presents a computational method for constructing Siegel sets for the action of \Gamma = SU(n; 1;O) on HnC, where O is the ring of integers of an imaginary quadratic field with trivial class group. The thesis first presents a basic algorithm for computing Siegel sets and then considers practical improvements which can be made to this algorithm in order to decrease computation time. This improved algorithm is implemented in a C++ program called siegel, the source code for which is freely available at http://code.google.com/p/siegel/, and this program is used to compute explicit Siegel sets for the action of all applicable groups \Gamma on H2C and H3C.

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Books on the topic "Hyperbolic space"

1

Elementary geometry in hyperbolic space. W. de Gruyter, 1989.

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2

Elstrodt, Jürgen, Fritz Grunewald, and Jens Mennicke. Groups Acting on Hyperbolic Space. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03626-6.

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Lax, Peter D. Hyperbolic systems of conservation laws in several space variables. Courant Institute of Mathematical Sciences, New York University, 1985.

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Elstrodt, J. Groups acting on hyperbolic space: Harmonic analysis and number theory. Springer, 1998.

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France, Société mathématique de, ed. Views of parameter space: Topographer and resident. Société mathématique de France, 2003.

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Sidilkover, David. A new time-space accurate scheme for hyperbolic problems I: Quasi-explicit case. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Glimm, James. Elementary waves for hyperbolic equations in higher space dimensions: an example from petroleum reservoir modeling. Courant Institute of Mathematical Sciences, New York University, 1985.

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W, Bates Peter. Existence and persistence of invariant manifolds for semiflows in Banach space. American Mathematical Society, 1998.

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Hyperbolic complex spaces. Springer, 1998.

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Kobayashi, Shoshichi. Hyperbolic complex spaces. Springer, 1998.

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Book chapters on the topic "Hyperbolic space"

1

Benedetti, Riccardo, and Carlo Petronio. "Hyperbolic Space." In Universitext. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-58158-8_1.

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Voight, John. "Hyperbolic space." In Graduate Texts in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56694-4_36.

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Gunn, Charlie. "Visualizing Hyperbolic Space." In Computer Graphics and Mathematics. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77586-4_19.

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Catoni, Francesco, Dino Boccaletti, Roberto Cannata, Vincenzo Catoni, and Paolo Zampetti. "Hyperbolic Numbers." In Geometry of Minkowski Space-Time. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17977-8_2.

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Elstrodt, Jürgen, Fritz Grunewald, and Jens Mennicke. "Three-Dimensional Hyperbolic Space." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03626-6_1.

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Kapovich, Michael. "Geometry of Hyperbolic Space." In Hyperbolic Manifolds and Discrete Groups. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4913-5_3.

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Ratcliffe, John G. "Isometries of Hyperbolic Space." In Foundations of Hyperbolic Manifolds. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31597-9_5.

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Ratcliffe, John G. "Isometries of Hyperbolic Space." In Foundations of Hyperbolic Manifolds. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4757-4013-4_5.

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Catoni, Francesco, Dino Boccaletti, Roberto Cannata, Vincenzo Catoni, and Paolo Zampetti. "Equilateral Hyperbolas and Triangles in the Hyperbolic Plane." In Geometry of Minkowski Space-Time. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17977-8_5.

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Bonahon, Francis. "The 3-dimensional hyperbolic space." In The Student Mathematical Library. American Mathematical Society, 2009. http://dx.doi.org/10.1090/stml/049/09.

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Conference papers on the topic "Hyperbolic space"

1

Phillips, Mark, and Charlie Gunn. "Visualizing hyperbolic space." In the 1992 symposium. ACM Press, 1992. http://dx.doi.org/10.1145/147156.147206.

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Kleinberg, R. "Geographic Routing Using Hyperbolic Space." In IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications. IEEE, 2007. http://dx.doi.org/10.1109/infcom.2007.221.

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Casey, Stephen. "Network Tomography in Hyperbolic Space." In 2019 13th International conference on Sampling Theory and Applications (SampTA). IEEE, 2019. http://dx.doi.org/10.1109/sampta45681.2019.9030912.

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Schmeier, Timothy, Joeseph Chisari, Sam Garrett, and Brett Vintch. "Music recommendations in hyperbolic space." In RecSys '19: Thirteenth ACM Conference on Recommender Systems. ACM, 2019. http://dx.doi.org/10.1145/3298689.3347029.

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KOKUBU, MASATOSHI. "HYPERBOLIC GAUSS MAPS AND PARALLEL SURFACES IN HYPERBOLIC THREE-SPACE." In Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277723_0016.

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Beşenk, Murat. "Digraphs on 3-dimensional hyperbolic space." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES (ICMRS 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5047903.

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Izumiya, Shyuichi, Donghe Pei, and Masatomo Takahashi. "Curves and surfaces in hyperbolic space." In Geometric Singularity Theory. Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-8.

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Timofeeva, Sofiia V., Dmitrii M. Sarkisian, Andrei M. Sukhov, and Sergey A. Zuev. "Greedy forwarding for hyperbolic space in MANET." In 2017 25th Telecommunication Forum (TELFOR). IEEE, 2017. http://dx.doi.org/10.1109/telfor.2017.8249291.

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Verbeek, Kevin, and Subhash Suri. "Metric Embedding, Hyperbolic Space, and Social Networks." In Annual Symposium. ACM Press, 2014. http://dx.doi.org/10.1145/2582112.2582139.

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López, Federico, Benjamin Heinzerling, and Michael Strube. "Fine-Grained Entity Typing in Hyperbolic Space." In Proceedings of the 4th Workshop on Representation Learning for NLP (RepL4NLP-2019). Association for Computational Linguistics, 2019. http://dx.doi.org/10.18653/v1/w19-4319.

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Reports on the topic "Hyperbolic space"

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Holzapfel, Rolf-Peter. Jacobi Theta Embedding of a Hyperbolic 4-Space with Cusps. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-11-63.

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Holzapfel, Rolf-Peter. Enumerative Geometry on Quasi-Hyperbolic 4-Spaces with Cusps. GIQ, 2012. http://dx.doi.org/10.7546/giq-4-2003-42-87.

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Berenstein, Carlos A., and Enrico C. Tarabusi. Range of the k-Dimensional Radon Transform in Real Hyperbolic Spaces. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada454845.

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