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arXiv · 1211.0949

Willmore-Helfrich L^{2}-flow of curves with natural boundary conditions

Anna Dall'Acqua·Paola Pozzi
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Abstract

We consider regular open curves in R^n with fixed boundary points and moving according to the L^{2}-gradient flow for a generalisation of the Helfrich functional. Natural boundary conditions are imposed along the evolution. More precisely, at the boundary the curvature vector is equal to the normal projection of a fixed given vector. A long-time existence result together with subconvergence to critical points is proven.

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Anna Dall'Acqua, Paola Pozzi. 2013-02-03. Willmore-Helfrich L^{2}-flow of curves with natural boundary conditions. https://arxiv.org/abs/1211.0949

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