Reifenberg Flatness and Oscillation of the Unit Normal Vector
Classical Analysis and ODEs
2017-08-18 v1 Analysis of PDEs
Metric Geometry
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.
Cite
@article{arxiv.1708.05331,
title = {Reifenberg Flatness and Oscillation of the Unit Normal Vector},
author = {Simon Bortz and Max Engelstein},
journal= {arXiv preprint arXiv:1708.05331},
year = {2017}
}