English

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

R2 v1 2026-06-23T18:41:41.488Z