# 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.

**Synopsis:**

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.