A journey through harmonic functions

dc.contributorCortissoz Iriarte, Jean Carlos
dc.contributorMalakhaltsev, Mikhail A.
dc.contributorVargas Domínguez, Andrés
dc.creatorPeters Stein, Daniel
dc.date.accessioned2023-01-23T21:24:04Z
dc.date.accessioned2023-09-07T00:06:41Z
dc.date.available2023-01-23T21:24:04Z
dc.date.available2023-09-07T00:06:41Z
dc.date.created2023-01-23T21:24:04Z
dc.date.issued2022-12-09
dc.identifierhttp://hdl.handle.net/1992/64079
dc.identifierinstname:Universidad de los Andes
dc.identifierreponame:Repositorio Institucional Séneca
dc.identifierrepourl:https://repositorio.uniandes.edu.co/
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8727113
dc.description.abstractIn the present work we concentrate on the study of harmonic functions on Riemannian manifolds. For this purpose we carry out a study of them starting with the classical Liouville theorem in the complex plane through its generalization in the Euclidean space and finally on Riemannian manifolds using Yau's gradient estimate. From there we find a method to understand the asymptotic behavior of harmonic functions on unbounded rotationally symmetric surfaces and, moreover, what consequences it has on the existence of non-constant bounded harmonic functions on this type of surfaces. Finally we concentrate on showing the duality that exists between the study of the growth of asymptotic functions and the Dirichlet problem at infinity.
dc.languageeng
dc.publisherUniversidad de los Andes
dc.publisherMaestría en Matemáticas
dc.publisherFacultad de Ciencias
dc.publisherDepartamento de Matemáticas
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dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.rightshttps://repositorio.uniandes.edu.co/static/pdf/aceptacion_uso_es.pdf
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightshttp://purl.org/coar/access_right/c_abf2
dc.titleA journey through harmonic functions
dc.typeTrabajo de grado - Maestría


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