Immersions with bounded second fundamental form

Patrick Breuning

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arXiv · 1201.4562

Immersions with bounded second fundamental form

Patrick Breuning

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Abstract

We first consider immersions on compact manifolds with uniform $L^p$-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.

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BibTeX RIS

Patrick Breuning. 2012-01-22. Immersions with bounded second fundamental form. https://arxiv.org/abs/1201.4562

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