Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $p$-Brunn-Minkowski inequalities for intrinsic volumes with $0\leq
  p<1$   We prove the validity of the $p$-Brunn-Minkowski inequality for the intrinsic
volume $V_k$, $k=2,\dots, n-1$, of convex bodies in $\mathbb{R}^n$, in a
neighborhood of the unit ball, for $0\le p<1$. We also prove that this
inequality does not hold true on the entire class of convex bodies of
$\mathbb{R}^n$, when $p$ is sufficiently close to $0$.

18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org