On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface
| Autor: | Cadavid, Carlos A., Osorno, María C., Ruíz, Óscar E. |
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| Přispěvatelé: | Universidad EAFIT. Departamento de Ingeniería Mecánica, Laboratorio CAD/CAM/CAE |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
OPERADORES DIFERENCIALES
Laplace transformation Mathematics::Spectral Theory TEORÍA DE MORSE Mathematics::Geometric Topology TRANSFORMACIONES DE LAPLACE Graph theory Manifolds (Mathematics) TEORÍA DE GRAFOS Functions of real variables TEORÍA DEL PUNTO CRÍTICO (ANÁLISIS MATEMÁTICO) Morse theory GENERADORES DE FUNCIONES Differential operators FUNCIONES DE VARIABLE REAL Critical point theory (mathematical analysis) VARIEDADES (MATEMÁTICAS) Function generators |
| Zdroj: | Repositorio EAFIT Universidad EAFIT instacron:Universidad EAFIT |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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