Lectures on mean curvature flows in higher codimensions

Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10054

Handbook of geometric analysis, (1), 525-543, 2008
Mean curvature ows of hypersurfaces have been extensively studied and there are various di erent approaches and many beautiful results. However, relatively little is known about mean curvature ows of submanifolds of higher codimensions. This notes starts with some basic materials on submanifold geometry, and then introduces mean curvature ows 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 ows of two-dimensional surfaces in four-dimensional ambient spaces.
Mean curvature, Submanifold, Symplectomorphism, Geometric evolution equation
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@inproceedings{mu-tao2008lectures,
  title={Lectures on mean curvature  flows in higher codimensions    },
  author={Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821213703237899368},
  booktitle={Handbook of geometric analysis},
  number={1},
  pages={525-543},
  year={2008},
}
Mu-Tao Wang. Lectures on mean curvature flows in higher codimensions . 2008. In Handbook of geometric analysis. pp.525-543. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821213703237899368.
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