Calculus of Variations and Geometric Measure Theory
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M. Novaga - S. Okabe

Convergence to equilibrium of gradient flows defined on planar curves

created by novaga on 30 Apr 2013
modified on 10 Nov 2018


Published Paper

Inserted: 30 apr 2013
Last Updated: 10 nov 2018

Journal: J. Reine Angew. Math.
Volume: 733
Pages: 87-120
Year: 2017

ArXiv: 1306.1406 PDF


We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.


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