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arXiv · 2310.05596

Stability analysis for the anisotropic curve shortening flow of planar networks

Michael Gößwein·Matteo Novaga·Paola Pozzi
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Abstract

In this article we study the anisotropic curve shortening flow for a planar network of three curves with fixed endpoints and which meet in a triple junction. We show that the anisotropic curvature energy fulfills a Lojasiewicz-Simon gradient inequality and use this knowledge to derive stability results for the flow. Precisely, in our main theorem we show that for any initial data, which are $C^{2,\alpha}$-close to a (local) energy minimizer, the flow exists globally and converges to a possibly different energy minimum.

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Michael Gößwein, Matteo Novaga, Paola Pozzi. 2023-10-09. Stability analysis for the anisotropic curve shortening flow of planar networks. https://arxiv.org/abs/2310.05596

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