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arXiv · 1708.05331

Reifenberg Flatness and Oscillation of the Unit Normal Vector

Simon Bortz·Max Engelstein
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Abstract

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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Simon Bortz, Max Engelstein. 2017-08-17. Reifenberg Flatness and Oscillation of the Unit Normal Vector. https://arxiv.org/abs/1708.05331

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