Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A solution to the lower dimensional Busemann-Petty problem in the
  hyperbolic space   The lower dimensional Busemann-Petty problem asks whether origin symmetric
convex bodies in $\mathbb{R}^n$ with smaller volume of all $k$-dimensional
sections necessarily have smaller volume. As proved by Bourgain and Zhang, the
answer to this question is negative if $k>3$. The problem is still open for
$k=2,3$. In this article we formulate and completely solve the lower
dimensional Busemann-Petty problem in the hyperbolic space $\mathbb{H}^n$.

9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol