A Compactness Theorem for the Second Fundamental Form

Details A Compactness Theorem for the Second Fundamental Form A Compactness Theorem for the Second Fundamental Form

2010-06-29

arxiv.org/abs/1006.5697v4

Mathematics

Differential Geometry

19 pages; corrected errors and added references

Scientific paper

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.

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