Convergence to equilibrium of gradient flows defined on planar curves

Matteo Novaga; Shinya Okabe

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arXiv · 1306.1406

Convergence to equilibrium of gradient flows defined on planar curves

Matteo Novaga·Shinya Okabe

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Abstract

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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Matteo Novaga, Shinya Okabe. 2013-06-06. Convergence to equilibrium of gradient flows defined on planar curves. https://arxiv.org/abs/1306.1406

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