# 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.