Two balls maximize the third Neumann eigenvalue in hyperbolic space
Spectral Theory
2020-09-22 v1 Analysis of PDEs
Differential Geometry
Abstract
We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is maximal for the disjoint union of two geodesic balls, among domains of given volume. This extends a recent result by Bucur and Henrot in Euclidean space, while providing a new proof of a key step in their argument
Keywords
Cite
@article{arxiv.2009.09980,
title = {Two balls maximize the third Neumann eigenvalue in hyperbolic space},
author = {Pedro Freitas and Richard S. Laugesen},
journal= {arXiv preprint arXiv:2009.09980},
year = {2020}
}
Comments
27 pages, 1 figure