Differential Harnack estimates for backward heat equations with potentials under the Ricci flow |
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Authors: | Xiaodong Cao |
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Affiliation: | Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA |
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Abstract: | 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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Keywords: | Differential Harnack estimate Backward heat equation Ricci flow |
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