Mean curvature flows and isotopy problems

Details Mean curvature flows and isotopy problems Mean curvature flows and isotopy problems

2012-04-04

arxiv.org/abs/1204.0841v1

Mathematics

Differential Geometry

10 pages, contribution to "Survey in Differential Geometry"

Scientific paper

In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differential equations. Several global existence theorems and applications to isotopy problems in geometry and topology will be presented. The results are based on joint works of the author with his collaborators I. Medo\v{s}, K. Smoczyk, and M.-P. Tsui.

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