Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the KLS conjecture and Hardy-type inequalities   We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary
functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily
vanishing on the boundary $\partial \Omega$. This reduces the study of the
Neumann Poincar\'e constant on $\Omega$ to that of the cone and Lebesgue
measures on $\partial \Omega$; these may be bounded via the curvature of
$\partial \Omega$. A second reduction is obtained to the class of harmonic
functions on $\Omega$. We also study the relation between the Poincar\'e
constant of a log-concave measure $\mu$ and its associated K. Ball body
$K_\mu$. In particular, we obtain a simple proof of a conjecture of
Kannan--Lov\'asz--Simonovits for unit-balls of $\ell^n_p$, originally due to
Sodin and Lata{\l}a--Wojtaszczyk.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys