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Hamilton Type Gradient Estimates for a Heat Equation under the Ricci-harmonic Flow
Liang-Chu Chang
,
Nguyen Thac Dung
,
Chiung-Jue Anna Sung
Abstract
Our aim in this paper is to study the linear heat equation on a Riemannian manifold evolving by the Ricci-harmonic flow. We first show a Hamilton type gradient estimate for the positive solution of the heat equation, which allows us to derive a Harnack inequality. It is worthy to note that comparing with the Li-Yau type estimate by Bailesteanu [1], our gradient estimate can be obtained without any assumption on the harmonic quantity in the flow.