Curvature contraction flows in the sphere

Title: Curvature contraction flows in the sphere
Creator: McCoy, James A.
Relation: ARC.DP150100375 http://purl.org/au-research/grants/arc/DP150100375
Relation: Proceedings of the American Mathematical Society Vol. 146, Issue 3, p. 1243-1256
Publisher Link: http://dx.doi.org/10.1090/proc/13831
Publisher: American Mathematical Society
Resource Type: journal article
Date: 2018
Description: 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.
Subject: curvature flow; parabolic partial differential equation; hypersurface; axial symmetry; spherical geometry
Identifier: http://hdl.handle.net/1959.13/1437338
Identifier: uon:40315
Identifier: ISSN:0002-9939
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format