A Compactness Theorem for the Second Fundamental Form

Name: Work Video:
Duration: 3 min 30 s
Description: In this note we establish several versions of a compactness theorem for submanifolds. In particular we require only bounds on the second fundamental form and do not assume volume or diameter bounds. As an application we prove a compactness theorem for mean curvature flows and use it to construct smooth blow-up limits as singularity models.
Andrew A. Cooper
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