Calculus of Variations and Geometric Measure Theory
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F. Palmurella - T. Rivière

The Parametric Approach to the Willmore Flow

created by palmurella on 02 May 2022
modified on 06 May 2022


Published Paper

Inserted: 2 may 2022
Last Updated: 6 may 2022

Journal: Adv. Math.
Volume: 400
Pages: 108257
Year: 2022
Doi: 10.1016/j.aim.2022.108257

ArXiv: 2012.11419 PDF


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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