The Parametric Approach to the Willmore Flow
Analysis of PDEs
2022-05-04 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2012.11419,
title = {The Parametric Approach to the Willmore Flow},
author = {Francesco Palmurella and Tristan Rivière},
journal= {arXiv preprint arXiv:2012.11419},
year = {2022}
}
Comments
Revised version to appear in Adv. Math