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Dissertations / Theses on the topic 'Geometric inequality'

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Published: 4 June 2025
Last updated: 1 August 2025

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1

Wink, Matthias. "Ricci solitons and geometric analysis." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:3aae2c5e-58aa-42da-9a1b-ec15cacafdad.

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This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. This work provides a rigorous construction thereof. A Lyapunov function is introduced to prove that the Ricci soliton metrics lie in a bounded region of an associated phase space. This also gives an a
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2

Wigren, Thomas. "The Cauchy-Schwarz inequality : Proofs and applications in various spaces." Thesis, Karlstads universitet, Avdelningen för matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-38196.

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We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.
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3

Hoffmann-Ostenhof, M., T. Hoffmann-Ostenhof, A. Laptev, and thoffman@esi ac at. "A Geometrical Version of Hardy's Inequality." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1017.ps.

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4

Van, Wyk Hans-Werner. "The Blaschke-Santalo inequality." Pretoria : [s.n.], 2007. http://upetd.up.ac.za/thesis/available/etd-06112008-165838.

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5

Santos, Ednaldo Sena dos. "Problemas de máximo e mínimo na geometria euclidiana /." Universidade Federal da Paraí­ba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7390.

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Made available in DSpace on 2015-05-15T11:46:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-08-27<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This work presents a research on problems of maxima and minima of the Euclidean geometry. Initially we present some preliminary results followed by statements that in essence use basic concepts of geometry. Below are some problems of maximizing area and minimizing perimeter of triangles and convex polygons, culminating in a proof of the isoperimetric inequality for polygons and review the general case. Sol
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6

Brito, Frank Werlly Mendes de. "Otimização: uma aplicação para desigualdade das médias e para desigualdade de Cauchy-Schwarz." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9347.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-30T15:23:43Z No. of bitstreams: 1 arquivototal.pdf: 822546 bytes, checksum: 65e4e4556f8a395ac8f52a971bc3fc38 (MD5)<br>Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-08-31T10:51:03Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 822546 bytes, checksum: 65e4e4556f8a395ac8f52a971bc3fc38 (MD5)<br>Made available in DSpace on 2017-08-31T10:51:03Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 822546 bytes, checksum: 65e4e4556f8a395ac8f52a971bc3fc38 (MD5) Previous issue date: 2016-02-29<br>
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7

Sumi, Ken. "Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263432.

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8

Lima, Josenildo da Cunha. "O estudo de problemas de otimização com a utilização do software GeoGebra." Universidade Estadual da Paraíba, 2017. http://tede.bc.uepb.edu.br/jspui/handle/tede/2871.

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Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2017-11-06T12:17:01Z No. of bitstreams: 1 PDF - Josenildo da Cunha Lima.pdf: 21330682 bytes, checksum: b04b7f38635dc46f7b4cfbfc949c318b (MD5)<br>Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-11-08T16:45:20Z (GMT) No. of bitstreams: 1 PDF - Josenildo da Cunha Lima.pdf: 21330682 bytes, checksum: b04b7f38635dc46f7b4cfbfc949c318b (MD5)<br>Made available in DSpace on 2017-11-08T16:45:20Z (GMT). No. of bitstreams: 1 PDF - Josenildo da Cunha Lima.pdf: 21330682 bytes, checksum: b04b7f38635dc46f7b4cfbfc949c318b (MD
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9

Pryby, Christopher Ian. "Some results on sums and products." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53090.

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We demonstrate new results in additive combinatorics, including a proof of a conjecture by J. Solymosi: for every epsilon > 0, there exists delta > 0 such that, given n² points in a grid formation in R², if L is a set of lines in general position such that each line intersects at least n^{1-delta} points of the grid, then |L| < n^epsilon. This result implies a conjecture of Gy. Elekes regarding a uniform statistical version of Freiman's theorem for linear functions with small image sets.
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10

Tramel, Rebecca. "New stability conditions on surfaces and new Castelnuovo-type inequalities for curves on complete-intersection surfaces." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20990.

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Let X be a smooth complex projective variety. In 2002, [Bri07] defined a notion of stability for the objects in Db(X), the bounded derived category of coherent sheaves on X, which generalized the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on X and the geometry of the variety. In 2012, [BMT14] gave a conjectural stability condition for threefolds. In the case that X is a complete intersection threefold, the existence of this stability condition would imply a Castelnuovo-type inequality for curves on X. I give a new Castel
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11

Hamer, Jesse A. "On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6587.

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We investigate various forms of link positivity: braid positivity, strong quasipositivity, and quasi- positivity. On the one hand, this investigation is undertaken in the context of braid simplification: we give sufficient conditions under which a given braid word is conjugate to a braid word with strictly fewer negative bands. On the other hand, we use the famous Bennequin inequality to define a new link invariant: the defect of the Bennequin inequality, or 3-defect, and give criteria in terms of the 3-defect under which a given link is (strongly) quasipositive. Moreover, we use the 4-dimensi
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12

Franceschi, Valentina. "Sharp and Quantitative Isoperimetric Inequalities in Carnot-Carathéodory spaces." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424812.

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This thesis is dedicated to the study of isoperimetric inequalities in some Carnot-Carathéodory spaces, related to the Heisenberg geometry. The thesis is organized as follows. Chapter 1 is concerned with some preliminaries: we consider Carnot-Carathéodory spaces, and we define Grushin spaces and H-type groups. Then, we introduce the notion of X-perimeter, showing the validity of a non-sharp isoperimetric inequality. In Chapter 2, we study the sharp isoperimetric inequality in H-type groups and Grushin spaces. Several techniques are needed here, such as representation formulas for the X-perime
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13

RIVA, ENEA. "Slope inequalities for fibred surfaces and fibreed threefolds." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/374266.

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Su una varieta algebrica fibrata si definesce un invariante relativo detto slope che ne specifica la natura. Per queste fibrazioni un ruolo importante è svolto del fibrato di Hodge e dagli invarianti geometrici delle fibre generiche. In particulare in questa tesi ci concentreremo su superfici e threefold fibrati su curve, dando un stima dal basso della slope che dipenda del rango unitario del fibrato di hodge e da: - indice di clifford cella curva generale, nel caso di superfici; -dal genere geometrico ($p_{g}$) della superficie generale nel caso di threefold. infine sfrutteremo i risultati ot
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14

Filho, Francisco de Assis Benjamim. "Desigualdades isoperimÃtricas para integrais de curvatura em domÃnios k-convexos estrelados." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6637.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico<br>Baseados nos trabalhos De Gerhardt e Urbas [12], [36], provamos um resultado de convergÃncia global e determinamos precisamente o comportamento assintÃtico de soluÃÃes de um fluxo geomÃtrico que descreve a evoluÃÃo de hipersuperfÃcies estreladas e k-convexas por funÃÃes das curvaturas principais. Como aplicaÃÃo, e seguindo o argumento de Guan e Li [16], utilizamos um caso particular deste resultado de convergÃncia para generalizar a clÃssica desigualdade de Alexandrov-Fenchel para domÃnios estrelados e k-convexos.<br>Based on the
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15

Oliveira, Josà AnastÃcio de. "Decaimento do primeiro autovalor do operador de Laplace-Beltrami em superfÃcies de nÃvel analÃticas na esfera." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17215.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior<br>FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico<br>Neste texto, serà apresentado um resultado proposto por Paulo Cordaro e Jorge Hounie sobre o decaimente do primeiro autovalor do operador de Laplace-Beltrami em uma superfÃcie de nÃvel conexa em Sn+1, n &#8805;1. Esta dissertaÃÃo baseia-se no artigo "The First Eingenvalue of Analytic Level Surfaces on Spheres"de Sagun Chanillo (Mathematical Reseach Letters, vol 1 (1994), p. 159-166).<br>In the text, will presented one resultad proposed by Paulo Cordaro and Jor
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16

Alexander, Matthew R. "Combinatorial and Discrete Problems in Convex Geometry." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1508949236617778.

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17

Pereira, Rosane Gomes. "Desigualdades universais para autovalores do polidrifting laplaciano em dominios compactos do R^n e S^n." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5542.

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Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-05-05T20:05:47Z No. of bitstreams: 2 Tese - Rosane Gomes Pereira - 2016.pdf: 1460804 bytes, checksum: bde81076cac51b848a33cb0c0f768798 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-05-06T11:39:46Z (GMT) No. of bitstreams: 2 Tese - Rosane Gomes Pereira - 2016.pdf: 1460804 bytes, checksum: bde81076cac51b848a33cb0c0f768798 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5)<br>Made availab
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18

Shiping, Liu. "Synthetic notions of curvature and applications in graph theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-102197.

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The interaction between the study of geometric and analytic aspects of Riemannian manifolds and that of graphs is a very amazing subject. The study of synthetic curvature notions on graphs adds new contributions to this topic. In this thesis, we mainly study two kinds of synthetic curvature notions: the Ollivier-Ricci cuvature on locally finite graphs and the combinatorial curvature on infinite semiplanar graphs. In the first part, we study the Ollivier-Ricci curvature. As known in Riemannian geometry, a lower Ricci curvature bound prevents geodesics from diverging too fast on average. We tra
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19

Myers, Ron Y. "The Effects of the Use of Technology In Mathematics Instruction on Student Achievement." FIU Digital Commons, 2009. http://digitalcommons.fiu.edu/etd/136.

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The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were th
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20

Aribi, Amine. "Le spectre du sous-laplacien sur les variétés CR strictement pseudoconvexes." Phd thesis, Université François Rabelais - Tours, 2012. http://tel.archives-ouvertes.fr/tel-00960234.

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Le but de cette thèse est d'étudier le spectre du sous-laplacien sur les variétés CR strictement peusdoconvexes. Nous prouvons que le spectre du sous-laplacien $\Delta_b$ est discret sur un domaine borné $\Omega \subset M$ d'une variété CR strictement pseudoconvexe qui satisfait l'inégalité de Poincaré, sous les conditions de Dirichlet au bord. Nous étudions le comportement des valeurs propres du sous-laplacien $\Delta_b$ sur une variété CR strictement pseudoconvexe compacte $M$, en tant que fonctionnelle sur l'espace ${\mathcal P}_+$ de formes de contact positivement orientées sur $M$ en dota
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21

Chen, Yun-Min, and 陳韻旻. "Growth and Inequality Effects of Fiscal Policies with Heterogeneous Quasi-Geometric Discounting." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/74018667700445732205.

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碩士<br>國立成功大學<br>經濟學系碩博士班<br>96<br>The paper investigates how fiscal policies affect economic growth and income inequality in an economy populated by heterogeneous agents with quasi-geometric discounting factor. Incorporating these assumptions pertaining to time preferences, this research aims to examine whether the invisible hand works or whether government’s regulation is preferable to laissez-faire fiscal policy in a two-sector neoclassical growth model. Theoretical and calibration results indicate that government’s fiscal instruments cannot vary agents’ effective discount factors. A laissez
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22

Indrei, Emanuel Gabriel. "Optimal transport, free boundary regularity, and stability results for geometric and functional inequalities." 2012. http://hdl.handle.net/2152/20631.

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We investigate stability for certain geometric and functional inequalities and address the regularity of the free boundary for a problem arising in optimal transport theory. More specifically, stability estimates are obtained for the relative isoperimetric inequality inside convex cones and the Gaussian log-Sobolev inequality for a two parameter family of functions. Thereafter, away from a ``small" singular set, local C^{1,\alpha} regularity of the free boundary is achieved in the optimal partial transport problem. Furthermore, a technique is developed and implemented for estimating the Hausdo
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23

Zemas, Konstantinos. "Geometric rigidity estimates for isometric and conformal maps from S^(n-1) to R^n." 2020. https://ul.qucosa.de/id/qucosa%3A73090.

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In this thesis we study qualitative as well as quantitative stability aspects of isometric and conformal maps from S^(n-1) to R^n, when n is greater or equal to 2 or 3 respectively. Starting from the classical theorem of Liouville, according to which the isometry group of S^(n-1) is the group of its rigid motions and the conformal group of S^(n-1) is the one of its Möbius transformations, we obtain stability results for these classes of mappings among maps from S^(n-1) to R^n in terms of appropriately defined deficits. Unlike classical geometric rigidity results for maps defined on domains o
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24

Rossi, Andrea. "Borell-Brascamp-Lieb inequalities: rigidity and stability." Doctoral thesis, 2018. http://hdl.handle.net/2158/1125503.

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La tesi è dedicata allo studio delle cosiddette disuguaglianze di Borell-Brascamp-Lieb, note in letteratura come forme funzionali della disuguaglianza di Brunn-Minkowski. L'intento della tesi è duplice: da una parte si prefigge come manuale dettagliato delle disuguaglianze di Borell-Brascamp-Lieb, affrontando varie estensioni e proprietà più o meno note in letteratura; in secondo luogo si concentra sulla questione della stabilità di tali disuguaglianze, cita
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25

Van, Wyk Hans-Werner. "The Blaschke-Santaló inequality." Diss., 2008. http://hdl.handle.net/2263/25447.

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26

"Transversal Chern number inequality on Sasaki manifolds." 2010. http://library.cuhk.edu.hk/record=b5894435.

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Ma, Chit.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.<br>Includes bibliographical references (leaves 61-63).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.6<br>Chapter 2 --- Sasaki Geometry --- p.8<br>Chapter 2.1 --- Sasakian manifolds --- p.8<br>Chapter 2.2 --- Transversal Kahler geometry --- p.11<br>Chapter 2.3 --- Sasaki-Futaki invariant --- p.16<br>Chapter 2.3.1 --- Space of Kahler cone metric --- p.17<br>Chapter 2.3.2 --- Futaki invariant --- p.20<br>Chapter 2.3.3 --- A formula for volume variation --- p.27<br>Chapter 3 --- Toric Geometry
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27

Sun, Jian. "Kähler-Einstein metrics and Sobolev inequality /." 2000. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9965165.

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28

Yu, Wenhua. "Blowup rate control for solution of Jang's equation and its application on Penrose inequality." Thesis, 2019. https://doi.org/10.7916/d8-avnq-g588.

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We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS Σ is exactly −1/√λlog τ, where τ is the distance from Σ and λ is the principal eigenvalue of the MOTS stability operator of Σ. We also prove that the gradient of the solution is of order τ^(-1). Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.
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29

SIMONE, CIANI. "Intrinsic Harnack inequality for local weak solutions to an anisotropic parabolic equation." Doctoral thesis, 2022. http://hdl.handle.net/2158/1263325.

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We prove a Harnack inequality for non-negative solutions of a parabolic equation having an anisotropic slow diffusion. We study the propagation of support of solutions, through an iterative technique reminiscent of De Giorgi’s method and through the investigation of particular embeddings in anisotropic Sobolev spaces. At this point, we make an analysis of the natural scaling of the equation to reduce the problem to a Fokker-Planck equation and construct a self-similar Barenblatt solution thanks to finite speed of propagation. Then we exploit translation invariance to obtain positivity near
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30

Lam, Mau-Kwong George. "The Graph Cases of the Riemannian Positive Mass and Penrose Inequalities in All Dimensions." Diss., 2011. http://hdl.handle.net/10161/3857.

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<p>We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus proving the Riemannian positive mass theorem in this case. If the graph has convex horizons, we also prove the Riemannian Penrose inequality by giving a lower bound to the boundary integrals using the Aleksandrov-Fenchel inequality. We also prove the ZAS inequality for graphs in Min
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31

Shartser, Leonid. "De Rham Theory and Semialgebraic Geometry." Thesis, 2011. http://hdl.handle.net/1807/29865.

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This thesis consists of six chapters and deals with four topics related to De Rham Theory on semialgebraic sets. The first topic deals with L-infinity cohomology on semialgebraic sets. We introduce smooth L-infinity differential forms on a singular (semialgebraic) space X in Rn. Roughly speaking, a smooth L-infinity differential form is a collection of smooth forms on disjoint smooth subsets (stratification) of X with matching tangential components on the adjacent strata and of bounded size (in the metric induced from Rn). We identify the singular homology of X as the homology of the chain co
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32

Ibrahim, Alawiah. "Some Inequalities Concerning Power Series and Their Interaction With Univalent Function Theory." Thesis, 2014. https://vuir.vu.edu.au/25359/.

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Power series are fundamental in the study of Geometric Function Theory. In fact, they constitute a major part in Complex Analysis. The purpose of this dissertation is to employ analytic functions defined by power series in two different directions. The first of these discussed in Part I, mainly contributes to Analytic Inequalities in Real and Complex Analysis, while the second direction discussed in Part II, deals with Analytic and Univalent Function Theory.
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Anglada, Pablo Rubén. "Desigualdades geométricas para objetos en relatividad general." Doctoral thesis, 2018. http://hdl.handle.net/11086/6552.

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Tesis (Doctor en Física)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación, 2018.<br>En este trabajo presentamos demostraciones formales de desigualdades geométricas relacionando la carga, la masa, el momento angular y el tamaño para objetos compactos, tanto para objetos ordinarios, como una estrella de neutrones, como para agujeros negros. Comenzamos estudiando un problema simple: la relación entre carga y tamaño en simetría esférica. Probamos que si tomamos un dato inicial que contiene un objeto ordinario cargado, dos veces el radio de área del objet
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34

Shiping, Liu. "Synthetic notions of curvature and applications in graph theory." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A11816.

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The interaction between the study of geometric and analytic aspects of Riemannian manifolds and that of graphs is a very amazing subject. The study of synthetic curvature notions on graphs adds new contributions to this topic. In this thesis, we mainly study two kinds of synthetic curvature notions: the Ollivier-Ricci cuvature on locally finite graphs and the combinatorial curvature on infinite semiplanar graphs. In the first part, we study the Ollivier-Ricci curvature. As known in Riemannian geometry, a lower Ricci curvature bound prevents geodesics from diverging too fast on average. We tra
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