Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $L_p$-Minkowski problem with super-critical exponents   The $L_p$-Minkowski problem deals with the existence of closed convex
hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed $p$-area measures. It
extends the classical Minkowski problem and embraces several important
geometric and physical applications. The Existence of solutions has been
obtained in the sub-critical case $p>-n-1$, but the problem remains widely open
in the super-critical case $p<-n-1$. In this paper, we introduce new ideas to
solve the problem for all the super-critical exponents. A crucial ingredient in
our proof is a topological method based on the calculation of the homology of a
topological space of ellipsoids.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin