Harnack estimate for the mean curvature flow
type: Item
instance of: scholarly article
title: Harnack estimate for the mean curvature flow
zbMATH Open document ID: 0827.53006
author: Richard S. Hamilton
published in: Journal of Differential Geometry
publication date: 1995-12-13T00:00:00Z
review text: The author derives a differential Harnack inequality for weakly convex solutions of the mean curvature flow. This flow is the evolution of a hypersurface \(M^n\) in Euclidean space \(\mathbb{R}^{n + 1}\) by its mean curvature. As an application he shows that any strictly convex solution of the flow which is defined for all times and such that the mean curvature assumes its maximum value must be a translating soliton, i.e. a surface evolving by translating in space with constant velocity. For the proof the author derives from the mean curvature flow equation explicit equations for the evolution of the second fundamental form and the basic Harnack expression.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 761189
zbMATH Keywords: Harnack inequality
zbMATH Keywords: mean curvature flow
Wikidata QID: Q115178702
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214456010
OpenAlex ID: W1569084793
DOI: 10.4310/JDG/1214456010
description: scientific article; zbMATH DE number 761189