Differential Harnack Estimates for Parabolic Equations

Details Differential Harnack Estimates for Parabolic Equations Differential Harnack Estimates for Parabolic Equations

2010-01-28

arxiv.org/abs/1001.5245v1

Proc. of Complex and Differential Geometry, 2010

Mathematics

Differential Geometry

10 pages

Scientific paper

Let $(M,g(t))$ be a solution to the Ricci flow on a closed Riemannian
manifold. In this paper, we prove differential Harnack inequalities for
positive solutions of nonlinear parabolic equations of the type $$\ppt f=\Delta
f-f \ln f +Rf.$$ We also comment on an earlier result of the first author on
positive solutions of the conjugate heat equation under the Ricci flow.

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