| 概要 | A family of k-dimensional surfaces in an n-dimensional
Euclidean space (or more generally in a Riemannian
manifold) is called the mean curvature flow (MCF) if the
velocity of motion is equal to its mean curvature. One
can define a weak notion of MCF using a language of
geometric measure theory called varifold. Recently we
proved a general local epsilon-regularity theorem in this
setting, which shows among other things almost everywhere
smoothness for the so called unit density MCF in
Riemannian manifold for any codimensions. The Allard
regularity theorem on generalized minimal submanifolds
turns out to be a special case of our theorem. I will
spend most time explaining the background materials and
main results, and sketch the outline of proof.
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