Immersions with Bounded Second Fundamental Form
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- Breuning, P. J Geom Anal (2015) 25: 1344. doi:10.1007/s12220-014-9472-7
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We first consider immersions on compact manifolds with uniform Lp-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.