Expansion of embedded curves with turning angle greater than \(-\pi\)
type: Item
instance of: scholarly article
title: Expansion of embedded curves with turning angle greater than \(-\pi\)
zbMATH Open document ID: 0858.53001
author: Bennett Chow
author: Lii-Perng Liou
author: Dong-Ho Tsai
published in: Inventiones Mathematicae
publication date: 1996-11-26T00:00:00Z
full work available at URL: https://eudml.org/doc/144353
review text: Recently, the first and third author [J. Differ. Geom., to appear] showed that closed convex curves in the plane expanding by a positive function of their curvature expand to infinity and become asymptotically round. The third author [Comm. Anal. Geom. 4, No. 3, 459-480 (1996)] extended this result to starshaped initial curves. Here the authors carry this a step further by showing that for a certain general class of closed embedded initial curves, the solutions become starshaped and then convex after a finite time, and then asymptotically round.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 922456
zbMATH Keywords: expansion
zbMATH Keywords: embedded curves
zbMATH Keywords: curvature flow
reviewed by: John Urbas
MaRDI profile type: Publication
OpenAlex ID: W4252401661
cites work: Contraction of convex hypersurfaces by their affine normal
cites work: On the formation of singularities in the curve shortening flow
cites work: Parabolic equations for curves on surfaces. I: Curves with \(p\)-integrable curvature
cites work: Parabolic equations for curves on surfaces. II: Intersections, blow-up and generalized solutions
cites work: The zero set of a solution of a parabolic equation.
cites work: On the affine heat equation for non-convex curves
cites work: Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
cites work: Aleksandrov reflection and geometric evolution of hypersurfaces
cites work: Geometric expansion of convex plane curves
cites work: The heat equation shrinking convex plane curves
cites work: Flow of nonconvex hypersurfaces into spheres
cites work: The heat equation shrinks embedded plane curves to round points
cites work: Flow by mean curvature of convex surfaces into spheres
cites work: Geometric expansion of starshaped plane curves
cites work: An expansion of convex hypersurfaces
cites work: On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
DOI: 10.1007/S002220050034
Recommended article: Q4668556
Recommended article: Expanding convex immersed closed plane curves
Recommended article: Geometric expansion of convex plane curves
Recommended article: Q5463692
Recommended article: Embedded curves and foliations
Recommended article: Embeddings of curves
Recommended article: Geometric expansion of starshaped plane curves
Recommended article: Embeddings of curves in the plane
Recommended article: A note on expansion of convex plane curves via inverse curvature flow
description: scientific article; zbMATH DE number 922456