Interior estimates and longtime solutions for mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
type: Item
instance of: scholarly article
title: Interior estimates and longtime solutions for mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
zbMATH Open document ID: 0909.53045
author: Klaus Ecker
published in: Journal of Differential Geometry
publication date: 1999-03-25T00:00:00Z
review text: For entire graphs defining spacelike hypersurfaces in Minkowski space which are moving by mean curvature, the author proves the following Theorem: For any smooth initial data \(u_0:{\mathbb R}^n\to{\mathbb R}\) defining a spacelike hypersurface the mean curvature flow has a smooth spacelike solution for all \(t>0\). The proof is done by solving corresponding boundary value problems on increasing domains of radius \(k\) and selecting a converging subsequence of solutions for \(k\to\infty\). The longtime existence of solutions for these boundary value problems is shown in the first part of the paper by deriving appropriate interior estimates.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1145658
zbMATH Keywords: mean curvature flow
zbMATH Keywords: Minkowski space
zbMATH Keywords: spacelike hypersurface
zbMATH Keywords: longtime existence of solutions
zbMATH Keywords: interior estimates
reviewed by: Barbara Priwitzer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214459975
OpenAlex ID: W1598913697
Wikidata QID: Q115175558
DOI: 10.4310/JDG/1214459975
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description: scientific article; zbMATH DE number 1145658