Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The volume of the intersection of a convex body with its translates   It is proved that for a symmetric convex body K in R^n, if for some tau > 0,
|K cap (x+tau K)| depends on ||x||_K only, then K is an ellipsoid. As a part of
the proof, smoothness properties of convolution bodies ls are studied.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org