Reifenberg Flatness and Oscillation of the Unit Normal Vector
Simon Bortz, Max Engelstein · arXiv (Cornell University) · 2017
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.