Differential Harnack estimates for positive solutions to heat equation under Finsler–Ricci flow

Sajjad Lakzian

Vol. 278 (2015), No. 2, 447–462

DOI: 10.2140/pjm.2015.278.447

Abstract

We prove first order differential Harnack estimates for positive solutions of the heat equation (in the sense of distributions) under closed Finsler–Ricci flows. We assume suitable Ricci curvature bounds throughout the flow and also assume that the $S$-curvature vanishes along the flow. One of the key tools we use is the Bochner identity for Finsler structures proved by Ohta and Sturm (Adv. Math. 252 (2014), 429–448).

Keywords

Finsler–Ricci flow, differential Harnack, gradient estimate, weighted Ricci curvature, heat equation, curvature-dimension

Mathematical Subject Classification 2010

Primary: 35K55

Secondary: 53C21

Milestones

Received: 8 May 2014

Revised: 10 March 2015

Accepted: 30 April 2015

Published: 6 October 2015