Equilibrium solutions to generalized motion by mean curvature
type: Item
instance of: scholarly article
title: Equilibrium solutions to generalized motion by mean curvature
zbMATH Open document ID: 0941.35028
DOI: 10.1007/BF02922673
author: Tom Ilmanen
author: Peter Sternberg
author: William P. Ziemer
published in: The Journal of Geometric Analysis
publication date: 1998-09-10T00:00:00Z
review text: We consider viscosity equilibria to the mean curvature level set flow with a Dirichlet condition. The main result shows that almost every level set of an equilibrium solution is analytic off of a singular set of Hausdorff dimension at most \(n-8\) and that these level sets are stationary and stable with respect to the area functional. A key tool developed is a maximum principle for solutions to obstacle problems where the obstacle consists of (viscosity) minimal surfaces. Convergence to equilibrium as \(t\to\infty\) is also established for the associated initial-boundary value problem.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1186409
zbMATH Keywords: level set flow
zbMATH Keywords: viscosity solutions
zbMATH Keywords: stable varifolds
zbMATH Keywords: minimal surfaces
zbMATH Keywords: obstacle problems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1186409