English

A Compactness Theorem for the Second Fundamental Form

Differential Geometry 2011-04-26 v4

Abstract

In this note we establish several versions of a compactness theorem for submanifolds. In particular we require only bounds on the second fundamental form and do not assume volume or diameter bounds. As an application we prove a compactness theorem for mean curvature flows and use it to construct smooth blow-up limits as singularity models.

Keywords

Cite

@article{arxiv.1006.5697,
  title  = {A Compactness Theorem for the Second Fundamental Form},
  author = {Andrew A Cooper},
  journal= {arXiv preprint arXiv:1006.5697},
  year   = {2011}
}

Comments

19 pages; corrected errors and added references

R2 v1 2026-06-21T15:42:35.814Z