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arXiv · 2012.11419

The Parametric Approach to the Willmore Flow

Francesco Palmurella·Tristan Rivière
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Abstract

We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities. We restrict in this first work to a small-energy regime and prove that, for small-energy weak immersions, the Cauchy problem in this class admits a unique solution.

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Francesco Palmurella, Tristan Rivière. 2020-12-21. The Parametric Approach to the Willmore Flow. https://doi.org/10.1016/j.aim.2022.108257

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