A generalization of Reifenberg's theorem in R^N for flat cones

Abstract

In this paper we prove that if a closed set in R^N is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi-Hölder equivalent to such a cone. This generalizes Reifenberg's Topological Disk Theorem in 1960 and G. David, T. De Pauw and T. Toro's result in 2008.

55 pages, 4 figures