Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Isoperimetric Result on High-Dimensional Spheres   We consider an extremal problem for subsets of high-dimensional spheres that
can be thought of as an extension of the classical isoperimetric problem on the
sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere
$\mathbb{S}^{m-1}$, and let $\mathbf{y}\in \mathbb{S}^{m-1}$ be a randomly
chosen point on the sphere. What is the measure of the intersection of the
$t$-neighborhood of the point $\mathbf{y}$ with the subset $A$? We show that
with high probability this intersection is approximately as large as the
intersection that would occur with high probability if $A$ were a spherical cap
of the same measure.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas