Tangent cones and regularity of real hypersurfaces

@inproceedings{Ghomi2010TangentCA,
  title={Tangent cones and regularity of real hypersurfaces},
  author={Mohammad Ghomi and Ralph Howard},
  year={2010}
}
We characterize C embedded hypersurfaces of R as the only locally closed sets with continuously varying flat tangent cones whose measuretheoretic-multiplicity is at most m < 3/2. It follows then that any (topological) hypersurface which has flat tangent cones and is supported everywhere by balls of uniform radius is C. In the real analytic case the same conclusion holds under the weakened hypothesis that each tangent cone be a hypersurface. In particular, any convex real analytic hypersurface X… CONTINUE READING

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