Published Paper
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Inserted: 31 jul 2020
Last Updated: 9 nov 2026
Journal: Calc. Var. PDE
Volume: 60
Number: 1
Pages: Paper n.56, 17 pp.
Year: 2021
Doi: https://doi.org/10.1007/s00526-020-01916-0
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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