Symmetric mean curvature flow on the n-sphere

Jingwen Chen

Symmetric mean curvature flow on the n-sphere

Differential Geometry 2023-10-26 v2 Analysis of PDEs

Authors: Jingwen Chen

Abstract

In this article, we generalize our previous results joint with Pedro Gaspar to higher dimensions, prove the existence of (infinitely many) eternal weak mean curvature flows in $S^{n+1}$ (for all $n \geq 2$ ) connecting a Clifford hypersurface $S^1(\sqrt{\frac{1}{n}}) \times S^{n-1} (\sqrt{\frac{n-1}{n}})$ to the equatorial spheres $S^n$ .

Keywords

mean curvature flow clifford hypersurface equatorial sphere weak flow eternal flow

Cite

@article{arxiv.2304.12282,
  title  = {Symmetric mean curvature flow on the n-sphere},
  author = {Jingwen Chen},
  journal= {arXiv preprint arXiv:2304.12282},
  year   = {2023}
}

Comments

19 pages, updated the proof of Lemma 2. arXiv admin note: text overlap with arXiv:2107.09140

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