Curvature flows in the sphere

Claus Gerhardt Ruprecht-Karls-Universität, Institut für Angewandte Mathematik

Differential Geometry mathscidoc:1609.10341

JDG, 100, (2), 301-347, 2015
We consider contracting and expanding curvature flows in $\Ss$. When the flow hypersurfaces are strictly convex we establish a relation between the contracting hypersurfaces and the expanding hypersurfaces which is given by the Gau{\ss} map. The contracting hypersurfaces shrink to a point $x_0$ while the expanding hypersurfaces converge to the equator of the hemisphere $\mc H(-x_0)$. 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 $C^\un(\Ss[n])$.
curvature flows, inverse curvature flows, contracting curvature flows, sphere, polar sets, dual flows, elementary symmetric polynomials
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  title={Curvature flows in the sphere},
  author={Claus Gerhardt},
Claus Gerhardt. Curvature flows in the sphere. 2015. Vol. 100. In JDG. pp.301-347.
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