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A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region

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arxiv 2409.03908 v3 pith:TMVTEXGF submitted 2024-09-05 math.AP math.SP

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classification math.APmath.SP
keywords dirichletmixedregionsmalleigenvaluefirstsufficientlyconnected
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We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give explicit examples of when the Dirichlet region is sufficiently small.

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  1. Hot spots in domains of constant curvature

    math.SP 2025-08 unverdicted novelty 6.0 of 10

    The hot spots conjecture holds for all non-acute geodesic triangles of constant negative curvature, with additional critical point and monotonicity results for other constant curvature triangles and polygons.

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