Comportamiento de funciones armónicas sobre variedades de curvatura negativa
ilustraciones, gráficas
- Autores:
-
Bravo Buitrago, John Edison
- Tipo de recurso:
- Fecha de publicación:
- 2022
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/84324
- Palabra clave:
- 510 - Matemáticas::515 - Análisis
Análisis armónico
Análisis funcional
Harmonic analysis
Functional analysis
Variedad diferenciable
Funciones Armónicas
Desigualdades diferenciales
Ecuación de Laplace
Problema de Dirichlet
Smooth Manifold
Harmonic Functions
Differential Inequalities
Laplace Equation
Dirichlet Problem
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| dc.title.translated.eng.fl_str_mv |
Behavior of harmonic functions on manifolds of negative curvature |
| title |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| spellingShingle |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa 510 - Matemáticas::515 - Análisis Análisis armónico Análisis funcional Harmonic analysis Functional analysis Variedad diferenciable Funciones Armónicas Desigualdades diferenciales Ecuación de Laplace Problema de Dirichlet Smooth Manifold Harmonic Functions Differential Inequalities Laplace Equation Dirichlet Problem |
| title_short |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| title_full |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| title_fullStr |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| title_full_unstemmed |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| title_sort |
Comportamiento de funciones armónicas sobre variedades de curvatura negativa |
| dc.creator.fl_str_mv |
Bravo Buitrago, John Edison |
| dc.contributor.advisor.none.fl_str_mv |
Cortissoz Iriarte, Jean Carlos |
| dc.contributor.author.none.fl_str_mv |
Bravo Buitrago, John Edison |
| dc.contributor.other.none.fl_str_mv |
Rodríguez Blanco, Guillermo |
| dc.contributor.orcid.spa.fl_str_mv |
Bravo Buitrago, John Edison [0001823088] |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::515 - Análisis |
| topic |
510 - Matemáticas::515 - Análisis Análisis armónico Análisis funcional Harmonic analysis Functional analysis Variedad diferenciable Funciones Armónicas Desigualdades diferenciales Ecuación de Laplace Problema de Dirichlet Smooth Manifold Harmonic Functions Differential Inequalities Laplace Equation Dirichlet Problem |
| dc.subject.lemb.spa.fl_str_mv |
Análisis armónico Análisis funcional |
| dc.subject.lemb.eng.fl_str_mv |
Harmonic analysis Functional analysis |
| dc.subject.proposal.spa.fl_str_mv |
Variedad diferenciable Funciones Armónicas Desigualdades diferenciales Ecuación de Laplace Problema de Dirichlet |
| dc.subject.proposal.eng.fl_str_mv |
Smooth Manifold Harmonic Functions Differential Inequalities Laplace Equation Dirichlet Problem |
| description |
ilustraciones, gráficas |
| publishDate |
2022 |
| dc.date.issued.none.fl_str_mv |
2022-07-25 |
| dc.date.accessioned.none.fl_str_mv |
2023-07-27T17:00:25Z |
| dc.date.available.none.fl_str_mv |
2023-07-27T17:00:25Z |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
| dc.type.content.spa.fl_str_mv |
Text |
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http://purl.org/redcol/resource_type/TM |
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acceptedVersion |
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https://repositorio.unal.edu.co/handle/unal/84324 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/84324 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
| dc.relation.references.spa.fl_str_mv |
M. Anderson. “The Dirichlet problem at infinity for manifolds of negative curvature". J. Differ. Geom. 18, 701–721, (1983). M. Anderson and R. Schoen. “Positive harmonic functions on complete manifolds of negative curvature". Ann. Math. 2. 121, 429–461. , (1985). S. Y. Cheng and S. T. Yau. “Differential equations on Riemannian manifolds and their geometric applications" Comm. Pure Appl. Math. 28, 333–354, (1975). H. Choi. “In asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds" Trans. Am. Math. Soc. 281, 691–716, (1984). J. E. Bravo. J. C. Cortissoz. D. P. Stein. “Some Observations on Liouville’s Theorem on Surfaces and the Dirichlet Problem at Infinity" Lobachevskii Journal of Mathematics, Vol. 43, No. 1, pp. 71–77, (2022) J. C. Cortissoz. “A note on harmonic functions on surfaces" Am. Math. Mon. 123, 884–893, (2016). J. C. Cortissoz. "An Observation on the Dirichlet Problem at Infinity on Riemannian cones" arXiv:2111.11351 [math.DG], aceptado en Nagoya Math. J. (2021). M.A. Al-Gwaiz. “Sturm-Liouville Theory and its Applications" Springer Undergraduate Mathematics Series, (2007). B.G. Pachpatte. “Inequalities for Differential and Integral Equations" Mathematics in science and engineering 197, (1998). D. Gilbarg, N. S. Trudinger. “Ëlliptic Partial Differential Equations of Second Order" Reprint of the 1998 edition. Classics in Mathematics, Springer-Verlag, Berlin, (2001). G. Herglotz. “Über potenzreihen mit positivem, realem Teil im Einheitskreis" Ber. Verh. Sachs, Akad. Wiss., Math.-Phys. Kl. 63, (1911). R. Ji. “The asymptotic Dirichlet problems on manifolds with unbounded negative curvature" Math. Proc. Cambridge Phil. Soc. 167, 133–157, (2019). P. li. “Geometric Analysis" Vol. 134 of Cambridge Studies in Advanced Mathematics (Cambridge Univ. Press, Cambridge, (2012). J. Milnor. “On deciding whether a surface is parabolic or hyperbolic" Am. Math. Mon. 84, 43–46, (1977). Jost, Jörgen. “Riemannian geometry and geometric analysis" Springer International., (2017). L. Ni and L. F. Tam. “Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature" J. Differ. Geom. 64, 457–524, (2003). D. Sullivan. “The Dirichlet problem at infinity for a negatively curved manifold" J. Differ. Geom. 18, 723–732, (1983). Elias M. Stein, Rami Shakarchi. “Fourier analysis: an introduction" Princeton Lectures in Analysis, Volume 1. 18, (2003). S. T. Yau. “Harmonic functions on complete Riemannian manifolds" JComm. Pure Appl. Math. 28, 201–228, (1975). M. H. Protter, H. F. Weinberger,. “Maximum Principles in Differential Equations" PrenticeHall, Engle- wood Cliffs, NJ, (1967). |
| dc.rights.none.fl_str_mv |
Derechos reservados al autor, 2023 |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial-SinDerivadas 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial-SinDerivadas 4.0 Internacional Derechos reservados al autor, 2023 http://creativecommons.org/licenses/by-nc-nd/4.0/ http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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64 páginas |
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application/pdf |
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Universidad Nacional de Colombia |
| dc.publisher.program.spa.fl_str_mv |
Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
| dc.publisher.faculty.spa.fl_str_mv |
Facultad de Ciencias |
| dc.publisher.place.spa.fl_str_mv |
Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Universidad Nacional de Colombia |
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Atribución-NoComercial-SinDerivadas 4.0 InternacionalDerechos reservados al autor, 2023http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cortissoz Iriarte, Jean Carlosbddf218a35f638aa90c1b352ace59374Bravo Buitrago, John Edisona36acd1412b4d33f1be2d1ce264545e4Rodríguez Blanco, GuillermoBravo Buitrago, John Edison [0001823088]2023-07-27T17:00:25Z2023-07-27T17:00:25Z2022-07-25https://repositorio.unal.edu.co/handle/unal/84324Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficasEl propósito de esta tesis de maestría es estudiar la existencia de funciones armónicas acotadas no constantes, dando demostraciones novedosas con estimativos explícitos de versiones de teoremas, ahora ya clásicos, sobre la existencia de dichas funciones armónicas acotadas no constantes como demostraron Anderson y Sullivan en [1] y [17]. Entre los métodos usados en esta tesis está una generalización de la conocida desigualdad de Gronwall, la teoría de Sturm-Liouville y ecuación de Riccatti parecen dictar el comportamiento de la parte radial de las soluciones a la ecuación de Laplace obtenidas por el método de separación de variables en el caso de métricas obtenidas por productos torcidos (alabeados -warped en inglés). (Texto tomado de la fuente)The purpose of this master’s thesis is to study the existence of non-constant bounded harmonic functions, giving new proofs with explicit estimates of versions of theorems, now classical, on the existence of the said non-constant bounded harmonic functions as shown by Anderson and Sullivan in [1] and [17]. Among the methods used in this thesis is a generalization of the well-known Gronwall inequality, the Sturm-Liouville theory and Riccatti equation that seem to dictate the behavior of the radial part of the solutions to Laplace’s equation obtained by the method of separation of variables in the case of metrics obtained by twisted products called warped.MaestríaMagíster en Ciencias - Matemáticas64 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::515 - AnálisisAnálisis armónicoAnálisis funcionalHarmonic analysisFunctional analysisVariedad diferenciableFunciones ArmónicasDesigualdades diferencialesEcuación de LaplaceProblema de DirichletSmooth ManifoldHarmonic FunctionsDifferential InequalitiesLaplace EquationDirichlet ProblemComportamiento de funciones armónicas sobre variedades de curvatura negativaBehavior of harmonic functions on manifolds of negative curvatureTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMM. Anderson. “The Dirichlet problem at infinity for manifolds of negative curvature". J. Differ. Geom. 18, 701–721, (1983).M. Anderson and R. Schoen. “Positive harmonic functions on complete manifolds of negative curvature". Ann. Math. 2. 121, 429–461. , (1985).S. Y. Cheng and S. T. Yau. “Differential equations on Riemannian manifolds and their geometric applications" Comm. Pure Appl. Math. 28, 333–354, (1975).H. Choi. “In asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds" Trans. Am. Math. Soc. 281, 691–716, (1984).J. E. Bravo. J. C. Cortissoz. D. P. Stein. “Some Observations on Liouville’s Theorem on Surfaces and the Dirichlet Problem at Infinity" Lobachevskii Journal of Mathematics, Vol. 43, No. 1, pp. 71–77, (2022)J. C. Cortissoz. “A note on harmonic functions on surfaces" Am. Math. Mon. 123, 884–893, (2016).J. C. Cortissoz. "An Observation on the Dirichlet Problem at Infinity on Riemannian cones" arXiv:2111.11351 [math.DG], aceptado en Nagoya Math. J. (2021).M.A. Al-Gwaiz. “Sturm-Liouville Theory and its Applications" Springer Undergraduate Mathematics Series, (2007).B.G. Pachpatte. “Inequalities for Differential and Integral Equations" Mathematics in science and engineering 197, (1998).D. Gilbarg, N. S. Trudinger. “Ëlliptic Partial Differential Equations of Second Order" Reprint of the 1998 edition. Classics in Mathematics, Springer-Verlag, Berlin, (2001).G. Herglotz. “Über potenzreihen mit positivem, realem Teil im Einheitskreis" Ber. Verh. Sachs, Akad. Wiss., Math.-Phys. Kl. 63, (1911).R. Ji. “The asymptotic Dirichlet problems on manifolds with unbounded negative curvature" Math. Proc. Cambridge Phil. Soc. 167, 133–157, (2019).P. li. “Geometric Analysis" Vol. 134 of Cambridge Studies in Advanced Mathematics (Cambridge Univ. Press, Cambridge, (2012).J. Milnor. “On deciding whether a surface is parabolic or hyperbolic" Am. Math. Mon. 84, 43–46, (1977).Jost, Jörgen. “Riemannian geometry and geometric analysis" Springer International., (2017).L. Ni and L. F. Tam. “Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature" J. Differ. Geom. 64, 457–524, (2003).D. Sullivan. “The Dirichlet problem at infinity for a negatively curved manifold" J. Differ. Geom. 18, 723–732, (1983).Elias M. Stein, Rami Shakarchi. “Fourier analysis: an introduction" Princeton Lectures in Analysis, Volume 1. 18, (2003).S. T. Yau. “Harmonic functions on complete Riemannian manifolds" JComm. Pure Appl. Math. 28, 201–228, (1975).M. H. Protter, H. F. Weinberger,. “Maximum Principles in Differential Equations" PrenticeHall, Engle- wood Cliffs, NJ, (1967).EstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84324/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1072661695.2023.pdf1072661695.2023.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf1287134https://repositorio.unal.edu.co/bitstream/unal/84324/2/1072661695.2023.pdf84393b5cbc98dace1898615ce374a95fMD52THUMBNAIL1072661695.2023.pdf.jpg1072661695.2023.pdf.jpgGenerated Thumbnailimage/jpeg7828https://repositorio.unal.edu.co/bitstream/unal/84324/3/1072661695.2023.pdf.jpg1ee9dc16d5c803cc8e303098c3b2fefcMD53unal/84324oai:repositorio.unal.edu.co:unal/843242023-08-12 23:04:08.425Repositorio Institucional Universidad Nacional de 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