@inbook{8c77e02ccf884d94a10e9293acfe70aa,
title = "Sharp Poincar{\'e}-type inequality for the gaussian measure on the boundary of convex sets",
abstract = "A sharp Poincar{\'e}-type inequality is derived for the restriction of the Gaussian measure on the boundary of a convex set. In particular, it implies a Gaussian mean-curvature inequality and a Gaussian iso-second-variation inequality. The new inequality is nothing but an infinitesimal equivalent form of Ehrhard{\textquoteright}s inequality for the Gaussian measure. While Ehrhard{\textquoteright}s inequality does not extend to general CD(1, ∞) measures, we formulate a sufficient condition for the validity of Ehrhard-type inequalities for general measures on ℝn via a certain property of an associated Neumann-to-Dirichlet operator.",
author = "Kolesnikov, {Alexander V.} and Emanuel Milman",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",
year = "2017",
doi = "https://doi.org/10.1007/978-3-319-45282-1_15",
language = "الإنجليزيّة",
series = "Lecture Notes in Mathematics",
pages = "221--234",
booktitle = "Geometric Aspects of Functional Analysis",
}