A generalization of Reifenberg's theorem in $R^3$
Differential Geometry
2007-05-23 v1 Metric Geometry
Abstract
In 1960 Reifenberg proved the topological disc property. He showed that a subset of which is well approximated by -dimensional affine spaces at each point and at each (small) scale is locally a bi-H\"older image of the unit ball in . In this paper we prove that a subset of which is well approximated by a minimal cone at each point and at each (small) scale is locally a bi-H\"older deformation of a minimal cone. We also prove an analogous result for more general cones in
Cite
@article{arxiv.math/0607441,
title = {A generalization of Reifenberg's theorem in $R^3$},
author = {G. David and T. DePauw and T. Toro},
journal= {arXiv preprint arXiv:math/0607441},
year = {2007}
}