English

Immersions with bounded second fundamental form

Differential Geometry 2012-01-24 v1

Abstract

We first consider immersions on compact manifolds with uniform LpL^p-bounds on the second fundamental form and uniformly bounded volume. We show compactness in arbitrary dimension and codimension, generalizing a classical result of J. Langer. In the second part, this result is used to deduce a localized version, being more convenient for many applications, such as convergence proofs for geometric flows.

Keywords

Cite

@article{arxiv.1201.4562,
  title  = {Immersions with bounded second fundamental form},
  author = {Patrick Breuning},
  journal= {arXiv preprint arXiv:1201.4562},
  year   = {2012}
}
R2 v1 2026-06-21T20:08:06.461Z