Mean curvature flow in higher codimension

Details Mean curvature flow in higher codimension Mean curvature flow in higher codimension

2002-04-03

arxiv.org/abs/math/0204054v1

Mathematics

Differential Geometry

To appear in the proceedings of International Congress of Chinese Mathematicians 2001

Scientific paper

The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity, global existence and convergence of the flow in various ambient spaces and codimensions were proved. We shall explain the results obtained as well as the techniques involved. The potential applications in symplectic topology and mirror symmetry will also be discussed.

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