English

Shrinking doughnuts via variational methods

Differential Geometry 2017-08-30 v1

Abstract

We use variational methods and a modified curvature flow to give an alternative proof of the existence of a self-shrinking torus under mean curvature flow. As a consequence of the proof, we establish an upper bound for the weighted energy of our shrinking doughnuts.

Cite

@article{arxiv.1708.08808,
  title  = {Shrinking doughnuts via variational methods},
  author = {Gregory Drugan and Xuan Hien Nguyen},
  journal= {arXiv preprint arXiv:1708.08808},
  year   = {2017}
}

Comments

18 pages, 2 figures

R2 v1 2026-06-22T21:26:42.095Z