Compact Curve Shortening Flow Solutions Out of Non-Compact Curves

Author:

Bourni Theodora1,Reiris Martin2

Affiliation:

1. Department of Mathematics, University of Tennessee Knoxville , Knoxville, TN 37996-1320, USA

2. Facultad de Ciencias, Universidad de la República , Montevideo, Uruguay

Abstract

Abstract We construct a slingshot, that is a compact, embedded solution to curve shortening flow that comes out of a non compact curve and exists for a finite time.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference9 articles.

1. The zero set of a solution of a parabolic equation;Angenent;J. Reine Angew. Math.,1988

2. Shortening complete plane curves;Chou;J. Differential Geom.,1998

3. Mean curvature evolution of entire graphs;Ecker;Ann. of Math. (2),1989

4. Interior estimates for hypersurfaces moving by mean curvature;Ecker;Invent. Math.,1991

5. The heat equation shrinking convex plane curves;Gage;J. Differential Geom.,1986

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