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

View/ Open
Date
2012-05-30Author
Cadavid, Carlos A.
Osorno, María C.
Ruíz, Óscar E.
Metrics
Metadata
Show full item recordAbstract
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
Documents PDF

Editor URL
Science Journal of Physics, Volume 2012, pp 1-8DOI
10.7237/sjp/128Collections
- Artículos [45]