• Corpus ID: 30079002

Reifenberg Flatness and Oscillation of the Unit Normal Vector

@article{Bortz2017ReifenbergFA,
  title={Reifenberg Flatness and Oscillation of the Unit Normal Vector},
  author={Simon Bortz and Max Engelstein},
  journal={arXiv: Classical Analysis and ODEs},
  year={2017}
}
We show (under mild topological assumptions) that small oscillation of the unit normal vector implies Reifenberg flatness. We then apply this observation to the study of chord-arc domains and to a quantitative version of a two-phase free boundary problem for harmonic measure previously studied by Kenig-Toro. 
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