Immersions with Bounded Second Fundamental Form

By Patrick Breuning. 2012

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b37d693688857c88ffabe9858e5b3f92ed4092e6