We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, with 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.

Convergence to equilibrium of gradient flows defined on planar curves

Novaga, Matteo;
2017-01-01

Abstract

We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, with 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.
2017
Novaga, Matteo; Okabe, Shinya
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/884196
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