Remarks on the KLS conjecture and hardy-type inequalities

Alexander V. Kolesnikov, Emanuel Milman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 Poincaré 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 Poincaré 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–Lovász–Simonovits for unit-balls of ℓnp, originally due to Sodin and Latała–Wojtaszczyk.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar (GAFA) 2011-2013
Number of pages20
StatePublished - 2014

Publication series

NameLecture Notes in Mathematics
PublisherSpringer Verlag

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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