Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Blaschke-Lebesgue Theorem for the Cheeger constant   In this paper we prove a new extremal property of the Reuleaux triangle: it
maximizes the Cheeger constant among all bodies of (same) constant width. The
proof relies on a fine analysis of the optimality conditions satisfied by an
optimal Reuleaux polygon together with an explicit upper bound for the inradius
of the optimal domain. As a possible perspective, we conjecture that this
maximal property of the Reuleaux triangle holds for the first eigenvalue of the
$p$-Laplacian for any $p\in (1,+\infty)$ (the current paper covers the case
$p=1$ whereas the case $p=+\infty$ was already known).

12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th