Improved long time existence for the Willmore flow of surfaces of revolution with Dirichlet data

Sascha Eichmann

Improved long time existence for the Willmore flow of surfaces of revolution with Dirichlet data

Analysis of PDEs 2024-02-20 v2

Authors: Sascha Eichmann

Abstract

To avoid possible singularities in the Willmore flow, one usually works under an energy threshold provided by the Li-Yau inequality. Here we improve this threshold by also considering parts outside of a possible singularity together with Dirichlet boundary data. We work in the class of surfaces of revolution.

Keywords

Willmore flow surfaces of revolution Dirichlet boundary data Li-Yau inequality energy threshold singularities long time existence

Cite

@article{arxiv.2402.05580,
  title  = {Improved long time existence for the Willmore flow of surfaces of revolution with Dirichlet data},
  author = {Sascha Eichmann},
  journal= {arXiv preprint arXiv:2402.05580},
  year   = {2024}
}

Comments

Independently and at the same time the same result was achieved by Schlierf in arXiv:2402.07755 . This is now acknowledged in the new version

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