Harnack estimate for mean curvature flow on the sphere

Paul Bryan; Mohammad N. Ivaki

doi:10.4310/AJM.2020.V24.N1.A7

Harnack estimate for mean curvature flow on the sphere

Paul Bryan, Mohammad N. Ivaki

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider the evolution of hypersurfaces on the unit sphere Sⁿ⁺¹ by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying an Aleksandrov reflection argument, we classify convex, ancient solutions of the mean curvature flow on the sphere. c 2020 International Press.

Original language	English
Pages (from-to)	165-176
Number of pages	12
Journal	Asian Journal of Mathematics
Volume	24
Issue number	1
DOIs	https://doi.org/10.4310/AJM.2020.V24.N1.A7
Publication status	Published - Feb 2020

Keywords

Mean curvature flow
Ancient solutions
Aleksandrov reflection
Harnack estimate

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10.4310/AJM.2020.V24.N1.A7

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title = "Harnack estimate for mean curvature flow on the sphere",

abstract = "We consider the evolution of hypersurfaces on the unit sphere Sn+1 by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying an Aleksandrov reflection argument, we classify convex, ancient solutions of the mean curvature flow on the sphere. c 2020 International Press.",

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KW - Ancient solutions

KW - Aleksandrov reflection

KW - Harnack estimate

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Harnack estimate for mean curvature flow on the sphere

Abstract

Keywords

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