Immersions with bounded second fundamental form

2012/01/22 by Patrick Breuning, Breuning, Patrick · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.1201.4562

arxiv created 2012/01/22 · openalex publication_date 2012/01/22 · arxiv updated 2012/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Compactness Theorem for the Second Fundamental Form

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