Hot spots in convex hyperbolic planar domains with small eigenvalues

Lawford Hatcher

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arXiv · 2605.21621

Hot spots in convex hyperbolic planar domains with small eigenvalues

Lawford Hatcher

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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.

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BibTeX RIS

Lawford Hatcher. 2026-05-20. Hot spots in convex hyperbolic planar domains with small eigenvalues. https://arxiv.org/abs/2605.21621

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