Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
type: Item
instance of: scholarly article
title: Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
zbMATH Open document ID: 0899.53044
author: Bennett Chow
published in: Communications in Analysis and Geometry
publication date: 1998-10-28T00:00:00Z
review text: The author applies the Aleksandrov reflection principle in order to derive gradient estimates for geometric evolution equations. He considers two classes of examples. The first part deals with hypersurfaces moving in the direction of their normals whose speed is a function of the principal curvatures. The author proves a gradient estimate in the case of starshaped hypersurfaces expanding by non-homogeneous functions of curvature. In the second part on degenerate parabolic flows of locally conformally flat metrics, the author obtains a uniform gradient estimate for the logarithm of the conformal factor, extending a result of \textit{R.-G. Ye} [J. Differ. Geom. 39, 35-50 (1994; Zbl 0846.53027)] on the Yamabe flow.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 1127780
zbMATH Keywords: Aleksandrov reflection principle
zbMATH Keywords: geometric evolution equations
zbMATH Keywords: gradient estimate
zbMATH Keywords: degenerate parabolic flows
reviewed by: Barbara Priwitzer
MaRDI profile type: Publication
DOI: 10.4310/CAG.1997.V5.N2.A5
description: scientific article; zbMATH DE number 1127780