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

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.