Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General volumes in the Orlicz-Brunn-Minkowski theory and a related
  Minkowski Problem II   The general dual volume $\dveV(K)$ and the general dual Orlicz curvature
measure $\deV(K, \cdot)$ were recently introduced for functions $G: (0,
\infty)\times \sphere\rightarrow (0, \infty)$ and convex bodies $K$ in $\R^n$
containing the origin in their interiors. We extend $\dveV(K)$ and $\deV(K,
\cdot)$ to more general functions $G: [0, \infty)\times \sphere\rightarrow [0,
\infty)$ and to compact convex sets $K$ containing the origin (but not
necessarily in their interiors). Some basic properties of the general dual
volume and of the dual Orlicz curvature measure, such as the continuous
dependence on the underlying set, are provided. These are required to study a
Minkowski-type problem for the dual Orlicz curvature measure. We mainly focus
on the case when $G$ and $\psi$ are both increasing, thus complementing our
previous work.
  The Minkowski problem asks to characterize Borel measures $\mu$ on $\sphere$
for which there is a convex body $K$ in $\R^n$ containing the origin such that
$\mu$ equals $\deV(K, \cdot)$, up to a constant. A major step in the analysis
concerns discrete measures $\mu$, for which we prove the existence of convex
polytopes containing the origin in their interiors solving the Minkowski
problem. For general (not necessarily discrete) measures $\mu$, we use an
approximation argument. This approach is also applied to the case where $G$ is
decreasing and $\psi$ is increasing, and hence augments our previous work. When
the measures $\mu$ are even, solutions that are origin-symmetric convex bodies
are also provided under some mild conditions on $G$ and $\psi$. Our results
generalize several previous works and provide more precise information about
the solutions of the Minkowski problem when $\mu$ is discrete or even.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat