A generalization of Reifenberg's theorem in $R^3$

Details A generalization of Reifenberg's theorem in $R^3$ A generalization of Reifenberg's theorem in $R^3$

2006-07-18

arxiv.org/abs/math/0607441v1

Mathematics

Differential Geometry

Scientific paper

In 1960 Reifenberg proved the topological disc property. He showed that a subset of $R^n$ which is well approximated by $m$-dimensional affine spaces at each point and at each (small) scale is locally a bi-H\"older image of the unit ball in $R^m$. In this paper we prove that a subset of $R^3$ 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 $R^n$

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