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An unknottedness result for self shrinkers with multiple ends

Differential Geometry 2023-06-30 v5 Geometric Topology

Abstract

In this article we prove an unknottedness result for self shrinkers in R3\mathbb{R}^3 with multiple asymptotically conical ends which bound a handlebody in a natural sense, using the mean curvature flow. As a corollary of this and previous work, asymptotically conical self shrinkers with two ends are unknotted.

Cite

@article{arxiv.2011.09373,
  title  = {An unknottedness result for self shrinkers with multiple ends},
  author = {Alexander Mramor},
  journal= {arXiv preprint arXiv:2011.09373},
  year   = {2023}
}

Comments

Revisited and majorly revised. Results and exposition improved, including some new arguments/details added. Comments welcome!

R2 v1 2026-06-23T20:20:58.551Z