A finiteness theorem via the mean curvature flow with surgery

Abstract

In this article, we use the recently developed mean curvature flow with surgery for 2 convex hypersurfaces to prove several isotopy existence and finally extrinsic finiteness results (in the spirit of Cheeger's compactness theorem) for the space of 2 convex hypersurfaces in ${\mathbb{R}}^{n+1}$.

arXiv comment30 pages, but many figures. Comments welcome!