Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alexandrov-Fenchel type inequalities for convex hypersurfaces in
  hyperbolic space and in sphere   In this paper, firstly, inspired by Nat\'{a}rio's recent work \cite{Na}, we
use the isoperimetric inequality to derive some Alexandrov-Fenchel type
inequalities for closed convex hypersurfaces in the hyperbolic space $\H^{n+1}$
and in the sphere $\SS^{n+1}$. We also get the rigidity in the spherical case.
Secondly, we use the inverse mean curvature flow in sphere \cite{gerh,Mak-Sch}
to prove an optimal Sobolev type inequality for closed convex hypersurfaces in
the sphere.

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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc