@inbook{b4ba033d18db4eaab46184803304e83d,
title = "Remarks on the KLS conjecture and hardy-type inequalities",
abstract = "We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body Ω ⊂ ℝn, not necessarily vanishing on the boundary ∂Ω. This reduces the study of the Neumann Poincar{\'e} constant on Ω to that of the cone and Lebesgue measures on ∂Ω; these may be bounded via the curvature of ∂Ω. A second reduction is obtained to the class of harmonic functions on Ω. We also study the relation between the Poincar{\'e} constant of a log-concave measure μ and its associated K. Ball body Kμ. In particular, we obtain a simple proof of a conjecture of Kannan–Lov{\'a}sz–Simonovits for unit-balls of ℓnp, originally due to Sodin and Lata{\l}a–Wojtaszczyk.",
author = "Kolesnikov, {Alexander V.} and Emanuel Milman",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.",
year = "2014",
doi = "https://doi.org/10.1007/978-3-319-09477-9_18",
language = "الإنجليزيّة",
series = "Lecture Notes in Mathematics",
publisher = "Springer Verlag",
pages = "273--292",
booktitle = "Geometric Aspects of Functional Analysis",
}