Borell's formula for a Riemannian manifold and applications

Joseph Lehec

Published 2015-12-18Version 1

Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a convolution inequality on the sphere due to Carlen, Lieb and Loss.