Translator Disclaimer
June 2015 Curvature flows in the sphere
Claus Gerhardt
J. Differential Geom. 100(2): 301-347 (June 2015). DOI: 10.4310/jdg/1430744123

Abstract

We consider contracting and expanding curvature flows in $\mathbb{S}^{n+1}$. When the flow hypersurfaces are strictly convex we establish a relation between the contracting hypersurfaces and the expanding hypersurfaces which is given by the Gauß map. The contracting hypersurfaces shrink to a point $x_0$ while the expanding hypersurfaces converge to the equator of the hemisphere $\mathcal{H}(-x_0)$. After rescaling, by the same scale factor, the rescaled hypersurfaces converge to the unit spheres with centers $x_0$ resp. $-x_0$ exponentially fast in $C^{\infty} (\mathbb{S}^n)$.

Citation

Download Citation

Claus Gerhardt. "Curvature flows in the sphere." J. Differential Geom. 100 (2) 301 - 347, June 2015. https://doi.org/10.4310/jdg/1430744123

Information

Published: June 2015
First available in Project Euclid: 4 May 2015

zbMATH: 06451271
MathSciNet: MR3343834
Digital Object Identifier: 10.4310/jdg/1430744123

Rights: Copyright © 2015 Lehigh University

JOURNAL ARTICLE
47 PAGES


SHARE
Vol.100 • No. 2 • June 2015
Back to Top