Space-time formulation of Harnack inequalities for curvature flows of hypersurfaces |
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Authors: | Bennett Chow Sun-Chin Chu |
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Affiliation: | (1) School of Mathematics, University of Minnesota, 55455 Minneapolis, MN;(2) Department of Mathematics, University of California, Los Angeles, 90095 Los Angeles, CA |
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Abstract: | We consider the motion of hypersurfaces in Riemannian manifolds by their curvature vectors. We show that the Harnack quadratic is an affine second fundamental form of the space-time track of the hypersurface. Given a solution to the Ricci flow, we show that with respect to an appropriate metric on space-time, the space-slices evolve by mean curvature flow. This enables us to identify the Harnack quadratic for the mean curvature flow with the trace Harnack quadratic for the Ricci flow. |
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Keywords: | KeywordHeading" >Math Subject Classifications 53C21 58G11 35K55 |
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