Funciones de Morse minimales en el espacio dodecaédrico de Poincaré, vía la Ecuación del Calor

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dc.contributor.advisorCadavid Moreno, Carlos Alberto
dc.contributor.authorBernal Vera, Jhon Willington
dc.coverage.spatialMedellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degreeseng
dc.creator.degreeMagíster en Matemáticas Aplicadasspa
dc.creator.emailjbernal6@eafit.edu.cospa
dc.date.accessioned2015-05-28T15:21:39Z
dc.date.available2015-05-28T15:21:39Z
dc.date.issued2014
dc.description.abstractLet (M,g) be a compact, connected, without boundary riemannian manifold that is homogeneous, i.e. each pair of points p, q 2M have isometric neighborhoods -- This thesis is a another step towards an understanding of the extent to which it is true that for each “generic” initial condition f0, the solution to @f/@t = gf, f (·, 0) = f0 is such that for sufficiently large t, f (·, 0) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M -- In this thesis we show that for the Poincaré dodecahedral space this seems to hold if one allows a generic small perturbation of the metric -- Concretely, we consider an approximation of the spherical Poincaré dodecahedral space by a suitably weighted graph, calculate the eigenvalues and eigenvectors of its laplacian oparator, and study the critical point structure of eigenvectors of some of the first nonzero eigenvalues, and observe that they have the least possible number of critical pointsspa
dc.identifier.urihttp://hdl.handle.net/10784/5397
dc.language.isospaspa
dc.publisherUniversidad EAFITspa
dc.publisher.departmentEscuela de Ciencias. Departamento de Ciencias Básicasspa
dc.publisher.programMaestría en Matemáticas Aplicadasspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesseng
dc.rights.localAcceso abiertospa
dc.subjectEsfera de homología de Poincaréspa
dc.subjectPoincaré, Henri (1854 - 1912)spa
dc.subject.keywordMorse theoryspa
dc.subject.keywordSpherespa
dc.subject.keywordHeat equationspa
dc.subject.keywordKernel functionsspa
dc.subject.keywordGeometry, riemannianspa
dc.subject.keywordIsometrics (Mathematics)spa
dc.subject.keywordDifferential topologyspa
dc.subject.keywordCritical point theory (mathematical analysis)spa
dc.subject.keywordGraph theoryspa
dc.subject.lembTEORÍA DE MORSEspa
dc.subject.lembESFERAspa
dc.subject.lembTOPOLOGÍAspa
dc.subject.lembECUACIÓN DEL CALORspa
dc.subject.lembFUNCIONES DE KERNELspa
dc.subject.lembGEOMETRÍA DE RIEMANNspa
dc.subject.lembISOMETRÍA (MATEMÁTICAS)spa
dc.subject.lembTOPOLOGÍA DIFERENCIALspa
dc.subject.lembTEORÍA DEL PUNTO CRÍTICO (ANÁLISIS MATEMÁTICO)spa
dc.subject.lembTEORÍA DE GRAFOSspa
dc.titleFunciones de Morse minimales en el espacio dodecaédrico de Poincaré, vía la Ecuación del Calorspa
dc.typemasterThesiseng
dc.type.hasVersionacceptedVersioneng
dc.type.localTesis de Maestríaspa

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