Bochner formulas, functional inequalities and generalized Ricci flow
Differential Geometry
2022-07-13 v1 Probability
Abstract
As a consequence of the Bochner formula for the Bismut connection acting on gradients, we show sharp universal Poincar\'e and log-Sobolev inequalities along solutions to generalized Ricci flow. Using the two-form potential we define a twisted connection on spacetime which determines an adapted Brownian motion on the frame bundle, yielding an adapted Malliavin gradient on path space. We show a Bochner formula for this operator, leading to characterizations of generalized Ricci flow in terms of universal Poincar\'e and log-Sobolev type inequalities for the associated Malliavin gradient and Ornstein-Uhlenbeck operator.
Keywords
Cite
@article{arxiv.2207.05633,
title = {Bochner formulas, functional inequalities and generalized Ricci flow},
author = {Eva Kopfer and Jeffrey Streets},
journal= {arXiv preprint arXiv:2207.05633},
year = {2022}
}