Curvature flows in the sphere

By Claus Gerhardt. 2013

67 citations recorded by the source corpus.

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 $C^\un(\Ss[n])$.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3208a6728bbcc11d080c6b937ac5e0b642497c36

Citations in the corpus

• The Spherical Convex Floating Body (2014, unknown): “…of convex bodies in more general spaces, including the sphere, has seen tremendous progress over the last decades, see e.g. [1–3, 8, 25, 34, 63, 66, 74], and in recent years classical spherical convex geometry has made progress at a rapid pace, see [4] [9] [17] [20] [23] [24] [53] [56] [64] [80].”