Symmetric hypersurfaces in Riemannian manifolds contracting to Lie groups by their mean curvature (Q1908908)

Huisken proved that, under a strong convexity assumption, in Riemannian spaces a flow by mean curvature will contract a closed convex hypersurface to a point in finite time [\textit{G. Huisken}, Invent. Math. 84, 463-480 (1986; Zbl 0589.53058)]. The author generalizes the result of Huisken by showing that in a Riemannian space the flow by mean curvature of a hypersurface invariant under a subgroup of the isometry group of the ambient space will contract the hypersurface to this subgroup. This result is established under a certain technical assumption analogous to the convexity condition.