Hot spots in convex hyperbolic planar domains with small eigenvalues
Spectral Theory
2026-05-22 v1 Analysis of PDEs
Differential Geometry
Abstract
We prove a variant of Rauch's hot spots conjecture for hyperbolic planar domains with small Neumann or mixed Dirichlet-Neumann eigenvalues. We conclude, for instance, that on bounded convex domains in the hyperbolic plane with sufficiently large area, second Neumann Laplace eigenfunctions have no interior critical points.
Cite
@article{arxiv.2605.21621,
title = {Hot spots in convex hyperbolic planar domains with small eigenvalues},
author = {Lawford Hatcher},
journal= {arXiv preprint arXiv:2605.21621},
year = {2026}
}
Comments
8 pages, 0 figures