Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional versions of L_p-affine surface area and entropy inequalities   In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski
theory is a modern analogue of the classical Brunn Minkowski theory. A
cornerstone of this theory is the L_p-affine surface area for convex bodies.
Here, we introduce a functional form of this concept, for log concave and
s-concave functions. We show that the new functional form is a generalization
of the original L_p-affine surface area. We prove duality relations and affine
isoperimetric inequalities for log concave and s-concave functions. This leads
to a new inverse log-Sobolev inequality for s-concave densities.

20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
29
The categories of this paper are: funct-an