Paper · Jan 22, 2023
A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria
As on arXiv
Abstract
A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is monotone increasing under the area-decreasing condition of the map. The flow provides a natural homotopy of the corresponding map and leads to sharp criteria regarding the homotopic class of maps between complex projective spaces, and maps from spheres to complex projective spaces, among others.
Comments: 22 pages. The statement of Theorem 1.4 is corrected. Some typos are corrected
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- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.