Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex bodies of constant width in spaces of constant curvature and the
  extremal area of Reuleaux triangles   Extending Blaschke and Lebesgue's classical result in the Euclidean plane, it
has been recently proved in spherical and the hyperbolic cases, as well, that
Reuleaux triangles have the minimal area among convex domains of constant width
$D$. We prove an essentially optimal stability version of this statement in
each of the three types of surfaces of constant curvature. In addition, we
summarize the fundamental properties of convex bodies of constant width in
spaces of constant curvature, and provide a characterization in the hyperbolic
case in terms of horospheres.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin