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arXiv · 2207.05633

Bochner formulas, functional inequalities and generalized Ricci flow

Eva Kopfer·Jeffrey Streets
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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.

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Eva Kopfer, Jeffrey Streets. 2022-07-12. Bochner formulas, functional inequalities and generalized Ricci flow. https://arxiv.org/abs/2207.05633

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