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arXiv · 2007.16093

The Lojasiewicz-Simon inequality for the elastic flow

Carlo Mantegazza·Marco Pozzetta
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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.

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Carlo Mantegazza, Marco Pozzetta. 2020-07-31. The Lojasiewicz-Simon inequality for the elastic flow. https://doi.org/10.1007/s00526-020-01916-0

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