Immersions with bounded second fundamental form

Details Immersions with bounded second fundamental form Immersions with bounded second fundamental form

2012-01-22

arxiv.org/abs/1201.4562v1

Mathematics

Differential Geometry

Scientific paper

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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