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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

R2 v1 2026-06-23T21:08:20.997Z