The Lojasiewicz-Simon inequality for the elastic flow

Abstract

We define the elastic energy of smooth immersed closed curves in ${\mathbb{R}}^n$ as the sum of the length and the $L^2$-norm of the curvature, with respect to the length measure. We prove that the $L^2$-gradient flow of this energy smoothly converges asymptotically to a critical point. One of our aims was to the present the application of a Lojasiewicz-Simon inequality, which is at the core of the proof, in a quite concise and versatile way.

References in corpus (1)

• Convergence of elastic flows of curves into manifolds

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