Geometry and Geometric Analysis Working Group

\(C^{1,\alpha}\) Reifenberg Theorems for Sets and Measures

Speaker: Silvia Ghinassi, Stony Brook University

Location: Warren Weaver Hall 517

Date: Monday, October 15, 2018, 11 a.m.


We provide geometric sufficient conditions for Reifenberg flat sets with holes in \(\mathbb{R}^n\) to be parametrized by a \(C^{1,\alpha}\) map. The conditions use a Jones type square function and all statements are quantitative in that the Hölder and Lipschitz constants of the parametrizations depend on such a function. We use these results to prove sufficient conditions for higher order rectifiability of sets and measures in \(\mathbb{R}^n\). Key tools for the proof come from Guy David and Tatiana Toro's parametrization of Reifenberg flat sets (with holes) in the Hölder and Lipschitz categories.