Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Laugesen and Morpurgo   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.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
3
The categories of this paper are: physics