Reifenberg Flatness and Oscillation of the Unit Normal Vector

2017/08/17 by Simon Bortz, Bortz, Simon, Max Engelstein +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1708.05331

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.

Citations

• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

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• On the dimension drop for harmonic measure on uniformly non-flat Ahlfors-David regular boundaries

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