Abstract

With G. David and T. Toro, A Generalization of Reifenberg's Theorem in R ³.

In 1960 Reifenberg proved the topological disc property. He showed that a subset of Rⁿ which is well approximated by m-dimensional affine spaces at each point and at each (small) scale is locally the bi-Holder image of the unit ball in R^m. In this paper we prove that a subset of R³ which is well approximated by a minimal cone at each point and at each (small) scale is a bi-Holder deformation of a minimal cone. We also prove an analogous result for more general cones in Rⁿ.

With G. David and T. Toro, A Generalization of Reifenberg's Theorem in R 3.

With G. David and T. Toro, A Generalization of Reifenberg's Theorem in R ³.