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arXiv · 2412.06344

Convex sets can have interior hot spots

Jaume de Dios Pont
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Abstract

The hot spots conjecture asserts that for any convex bounded domain $\Omega$ in $\mathbb R^d$, the first non-trivial Neumann eigenfunction of the Laplace operator in $\Omega$ attains its maximum at the boundary. We construct counterexamples to the conjecture for all sufficiently large values of $d$. The construction is based on an extension of the conjecture from convex sets to log-concave measures.

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Jaume de Dios Pont. 2024-12-09. Convex sets can have interior hot spots. https://arxiv.org/abs/2412.06344

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