Harnack estimates for conjugate heat kernel on evolving manifolds

Xiaodong Cao, Hongxin Guo, Hung Tran

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Abstract

In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation provides a unified framework for some known results, in particular including corresponding results of Ni (J Geom Anal 14(1): 87–100, 2004), Perelman (arXiv:math.DG/0211159, 2002) and Tran (arXiv:1211.6448, 2012) as special cases. Moreover, it leads to new results in the setting of Ricci-Harmonic flow and mean curvature flow in Lorentzian manifolds with nonnegative sectional curvature.

Original languageEnglish
Pages (from-to)201-214
Number of pages14
JournalMathematische Zeitschrift
Volume281
Issue number1-2
DOIs
StatePublished - Oct 19 2015

Keywords

  • Primary 53C44

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