• 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}
}
• Published 17 August 2017
• Mathematics
• arXiv: Classical Analysis and ODEs
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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