English

On a classification theorem for self-shrinkers

Differential Geometry 2018-11-14 v1

Abstract

We generalize a classification result for self-shrinkers of the mean curvature flow with nonnegative mean curvature, which was obtained by T. Colding and W. Minicozzi, replacing the assumption on polynomial volume growth with a weighted L2L^2 condition on the norm of the second fundamental form. Our approach adopt the viewpoint of weighted manifolds and permits also to recover and to extend some others recent classification and gap results for self-shrinkers.

Keywords

Cite

@article{arxiv.1212.4037,
  title  = {On a classification theorem for self-shrinkers},
  author = {Michele Rimoldi},
  journal= {arXiv preprint arXiv:1212.4037},
  year   = {2018}
}

Comments

9 pages. To appear on Proc. Amer. Math. Soc

R2 v1 2026-06-21T22:55:45.604Z