The Parametric Approach to the Willmore Flow
arXiv:2012.11419 · doi:10.1016/j.aim.2022.108257
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.
Revised version to appear in Adv. Math