A note on hot-spots free subregions of convex domains
Analysis of PDEs
2026-01-26 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
The second eigenfunction of the Neumann Laplacian on convex, planar domains is considered. Inspired by the famous hot spots conjecture and a related result of Steinerberger, we show that potential critical points of this eigenfunction (and, in particular, interior ''hot spots'') cannot be located ''near the center'' of the domain. The region in which critical points are excluded is described explicitly.
Keywords
Cite
@article{arxiv.2506.22184,
title = {A note on hot-spots free subregions of convex domains},
author = {Jonathan Rohleder},
journal= {arXiv preprint arXiv:2506.22184},
year = {2026}
}