Calculus of Variations and Geometric Measure Theory
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G. Bellettini - M. Novaga

Curvature Evolution of Nonconvex Lens-Shaped Domains

created by novaga on 28 May 2009
modified on 10 Nov 2018


Published Paper

Inserted: 28 may 2009
Last Updated: 10 nov 2018

Journal: J. Reine Angew. Math.
Volume: 656
Pages: 17-46
Year: 2011

ArXiv: 0906.0166 PDF


We study the curvature flow of planar nonconvex lens-shaped domains, considered as special symmetric networks with two triple junctions. We show that the evolving domain becomes convex in finite time; then it shrinks homothetically to a point. Our theorem is the analog of the result of Grayson for curvature flow of closed planar embedded curves.


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