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Curvature contraction flows in the sphere

Journal Article


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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 the (n+1)-dimensional sphere. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.

Publication Date


  • 2017

Citation


  • McCoy, J. A. (2017). Curvature contraction flows in the sphere. Proceedings of the American Mathematical Society, Online First 1-14.

Scopus Eid


  • 2-s2.0-85041542210

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1927&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/925

Number Of Pages


  • 13

Start Page


  • 1

End Page


  • 14

Volume


  • Online First

Place Of Publication


  • United States

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 the (n+1)-dimensional sphere. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.

Publication Date


  • 2017

Citation


  • McCoy, J. A. (2017). Curvature contraction flows in the sphere. Proceedings of the American Mathematical Society, Online First 1-14.

Scopus Eid


  • 2-s2.0-85041542210

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1927&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/925

Number Of Pages


  • 13

Start Page


  • 1

End Page


  • 14

Volume


  • Online First

Place Of Publication


  • United States