Bounding dimension of ambient space by density for mean curvature flow

Details Bounding dimension of ambient space by density for mean curvature flow Bounding dimension of ambient space by density for mean curvature flow

2005-03-01

arxiv.org/abs/math/0503023v1

Mathematics

Differential Geometry

13 pages

Scientific paper

For an ancient solution of the mean curvature flow, we show that each time
slice M_t is contained in an affine subspace with dimension bounded in terms of
the density and the dimension of the evolving submanifold. Recall that an
ancient solution is a family M_t that evolves under mean curvature flow for all
negative time t.

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