Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow

Details Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow

2008-05-22

arxiv.org/abs/0805.3381v1

Mathematics

Differential Geometry

13 pages

Scientific paper

In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities for positive solutions of backward heat-type equations with potentials (including the conjugate heat equation) under the Ricci flow. We shall also derive Perelman's Harnack inequality for the fundamental solution of the conjugate heat equation under the Ricci flow.

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