With G. David and T. Toro, A Generalization of Reifenberg's Theorem inR3.
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 Rm. 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