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

We 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 manifolds

• Autores: Cadavid, Carlos A.; Osorno, María C.; Ruíz, Óscar E.
• Fecha de publicación: 2012
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/9530
• Acceso en línea: http://hdl.handle.net/10784/9530
• Palabra clave: TEORÍA DE GRAFOS; OPERADORES DIFERENCIALES; VARIEDADES (MATEMÁTICAS); FUNCIONES DE VARIABLE REAL; GENERADORES DE FUNCIONES; TRANSFORMACIONES DE LAPLACE; TEORÍA DEL PUNTO CRÍTICO (ANÁLISIS MATEMÁTICO); TEORÍA DE MORSE; Graph theory; Differential operators; Manifolds (Mathematics); Functions of real variables; Function generators; Laplace transformation; Critical point theory (mathematical analysis); Morse theory; Graph theory; Differential operators; Manifolds (Mathematics); Functions of real variables; Function generators; Laplace transformation; Critical point theory (mathematical analysis); Morse theory
• License: Acceso abierto