Curvature contraction flows in the sphere
Open Access
- 30 October 2017
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 146 (3), 1243-1256
- https://doi.org/10.1090/proc/13831
Abstract
We show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of Sn+1. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.Keywords
Funding Information
- Australian Research Council (DP150100375)
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