Harnack estimates for nonlinear backward heat equations in geometric flows

Hongxin Guo, Masashi Ishida

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

Let M be a closed Riemannian manifold with a family of Riemannian metrics gij(t) evolving by a geometric flow ∂tgij=-2Sij, where Sij(t) is a family of smooth symmetric two-tensors. We derive several differential Harnack estimates for positive solutions to the nonlinear backward heat-type equation f∂t=-δf+γflog f+aSf where a and γ are constants and S=gijSij is the trace of Sij. Our abstract formulation provides a unified framework for some known results proved by various authors, and moreover leads to new Harnack inequalities for a variety of geometric flows.

Original languageEnglish
Pages (from-to)2638-2662
Number of pages25
JournalJournal of Functional Analysis
Volume267
Issue number8
DOIs
Publication statusPublished - 2014 Oct 15

Keywords

  • Geometric flows
  • Harnack estimates
  • Nonlinear heat equations
  • Ricci flow

ASJC Scopus subject areas

  • Analysis

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