On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface

2016-10-212012-05-302276-6367http://hdl.handle.net/10784/9530We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifoldsapplication/pdfenginfo:eu-repo/semantics/openAccessOn the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surfaceinfo:eu-repo/semantics/articleTEORÍA DE GRAFOSOPERADORES DIFERENCIALESVARIEDADES (MATEMÁTICAS)FUNCIONES DE VARIABLE REALGENERADORES DE FUNCIONESTRANSFORMACIONES DE LAPLACETEORÍA DEL PUNTO CRÍTICO (ANÁLISIS MATEMÁTICO)TEORÍA DE MORSEGraph theoryDifferential operatorsManifolds (Mathematics)Functions of real variablesFunction generatorsLaplace transformationCritical point theory (mathematical analysis)Morse theoryGraph theoryDifferential operatorsManifolds (Mathematics)Functions of real variablesFunction generatorsLaplace transformationCritical point theory (mathematical analysis)Morse theoryAcceso abierto2016-10-21Cadavid, Carlos A.Osorno, María C.Ruíz, Óscar E.10.7237/sjp/128