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arXiv · 0807.4726

On a conjecture of Laugesen and Morpurgo

Mihai N. Pascu·Maria E. Gageonea
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Abstract

A well known conjecture of R. Laugesen and C. Morpurgo asserts that the diagonal element of the Neumann heat kernel of the unit ball in $\mathbb{R}^{n}$ ($n\geq1$) is a radially increasing function. In this paper, we use probabilistic arguments to settle this conjecture, and, as an application, we derive a new proof of the Hot Spots conjecture of J. Rauch in the case of the unit disk.

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Mihai N. Pascu, Maria E. Gageonea. 2008-07-29. On a conjecture of Laugesen and Morpurgo. https://arxiv.org/abs/0807.4726

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