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Reifenberg Flatness and Oscillation of the Unit Normal Vector

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arxiv 1708.05331 v1 pith:EBGWNFT4 submitted 2017-08-17 math.CA math.APmath.MG

Simon Bortz , Max Engelstein This is my paper · ORCID
classification math.CAmath.APmath.MG
keywords 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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  1. On the dimension drop for harmonic measure on uniformly non-flat Ahlfors-David regular boundaries

    math.AP 2026-01 conditional novelty 5.0 of 10

    For uniformly non-flat Ahlfors-David regular boundaries of dimension between n−1−δ0 and n−1 in R^n (n≥3), harmonic measure is concentrated on a set of dimension strictly less than the boundary dimension.

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