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Uniqueness of Weak Solutions of the Plateau Flow

Analysis of PDEs 2023-03-23 v1 Differential Geometry

Abstract

In this paper, we study the uniqueness of weak solutions of the Plateau flow, which was first introduced by Wettstein as a half-Laplacian heat flow and recently studied by Struwe using alternative methods. This geometric gradient flow is of interest due to its links with free boundary minimal surfaces and the Plateau problem. We obtain uniqueness of weak solutions of this flow under a natural condition on the energy, which answers positively a question raised by Struwe.

Keywords

Cite

@article{arxiv.2303.12650,
  title  = {Uniqueness of Weak Solutions of the Plateau Flow},
  author = {Christopher Wright},
  journal= {arXiv preprint arXiv:2303.12650},
  year   = {2023}
}

Comments

10 pages