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arXiv · 1408.4155

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, Perelman, and Tran 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.

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Xiaodong Cao, Hongxin Guo, Hung Tran. 2014-08-18. Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds. https://doi.org/10.1007/s00209-015-1479-7

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