Reifenberg Flatness and Oscillation of the Unit Normal Vector
classification
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math.APmath.MG
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flatnessnormaloscillationreifenbergunitvectorapplyassumptions
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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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