Preprint

Inserted: 14 may 2025
Last Updated: 29 may 2025

Year: 2025

Abstract:

We investigate the asymptotic stability of the length--penalized elastic flow of curves with boundary points constrained to the x-axis in $\mathbb R^2$. The main tool in our analysis is the Lojasiewicz-Simon inequality, which is used to prove that the flow smoothly converges to an elastica.

Keywords: Geometric evolution, elastic energy, stability, Lojasiewicz-Simon inequality

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• Stability_Di25