On a conjecture of Laugesen and Morpurgo

Details On a conjecture of Laugesen and Morpurgo On a conjecture of Laugesen and Morpurgo

2008-07-29

arxiv.org/abs/0807.4726v2

Mathematics

Probability

14 pages, 1 figure

Scientific paper

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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