Flat flow is motion by crystalline curvature for curves with crystalline energies
type: Item
instance of: scholarly article
title: Flat flow is motion by crystalline curvature for curves with crystalline energies
zbMATH Open document ID: 0867.58020
published in: Journal of Differential Geometry
publication date: 1996-03-20T00:00:00Z
review text: It is shown that, for interface energies which are crystalline, motion of curves in the plane by crystalline curvature typically coincides with their flat curvature flow. An interface energy function is called crystalline in the case that its equilibrium crystal shape (Wulff shape) is a polygon. Motion by crystalline curvature results from integration of coupled systems of ordinary differential equations as set forth independently in [\textit{S. Angenent} and \textit{M. E. Gurtin}, II: Arch. Ration. Mech. Anal. 108, No. 4, 323-391 (1989; Zbl 0723.73017) and \textit{J. E. Taylor}, Proc. Symp. Pure Math. 54, 417-438 (1993; Zbl 0823.49028)]. Flat curvature flows are the limits of sequences of variational minimizations as set forth in [\textit{F. Almgren, J. E. Taylor}, and \textit{L. Wang}, Curvature driven flows: A variational approach, SIAM J. Control Optimization 31, No. 2, 387-438 (1993; Zbl 0783.35002)].
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 844212
zbMATH Keywords: motion by mean curvature
zbMATH Keywords: crystalline surface energy
zbMATH Keywords: polygonal geometry
zbMATH Keywords: integral currents
zbMATH Keywords: crystalline curvature
zbMATH Keywords: variational minimizations
Wikidata QID: Q115178025
author: Frederick J. jun. Almgren
author: Jean E. Taylor
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214457030
OpenAlex ID: W1490202623
DOI: 10.4310/JDG/1214457030
description: scientific article; zbMATH DE number 844212