Lectures on mean curvature flows in higher codimensions

Details Lectures on mean curvature flows in higher codimensions Lectures on mean curvature flows in higher codimensions

2011-04-17

arxiv.org/abs/1104.3354v1

Handbook of geometric analysis. No. 1, 525-543, Adv. Lect. Math. (ALM), 7, 2008

Mathematics

Differential Geometry

19 pages

Scientific paper

Mean curvature flows of hypersurfaces have been extensively studied and there are various different approaches and many beautiful results. However, relatively little is known about mean curvature flows of submanifolds of higher codimensions. This notes starts with some basic materials on submanifold geometry, and then introduces mean curvature flows in general dimensions and co-dimensions. The related techniques in the so called "blow-up" analysis are also discussed. At the end, we present some global existence and convergence results for mean curvature flows of two-dimensional surfaces in four-dimensional ambient spaces.

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