On the first stability eigenvalue of closed submanifolds in the Euclidean and hyperbolic spaces

Antonio W. Cunha, Henrique F. de Lima, Fábio R. dos Santos
2017 Differential geometry and its applications  
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
more » ... of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifolds.
doi:10.1016/j.difgeo.2017.03.002 fatcat:5yppkp5yuvewxasx3xmukbrqva