Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of log-concave functions: the $L_p$ Asplund sum and the $L_{p}$
  Minkowski problem   The aim of this paper is to develop a basic framework of the $L_p$ theory for
the geometry of log-concave functions, which can be viewed as a functional
"lifting" of the $L_p$ Brunn-Minkowski theory for convex bodies. To fulfill
this goal, by combining the $L_p$ Asplund sum of log-concave functions for all
$p>1$ and the total mass, we obtain a Pr\'ekopa-Leindler type inequality and
propose a definition for the first variation of the total mass in the $L_p$
setting. Based on these, we further establish an $L_p$ Minkowski type
inequality related to the first variation of the total mass and derive a
variational formula which motivates the definition of our $L_p$ surface area
measure for log-concave functions. Consequently, the $L_p$ Minkowski problem
for log-concave functions, which aims to characterize the $L_p$ surface area
measure for log-concave functions, is introduced. The existence of solutions to
the $L_p$ Minkowski problem for log-concave functions is obtained for $p>1$
under some mild conditions on the pre-given Borel measures.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn