Porosity and Differentiability

Gareth Speight

Event: ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis

Date: Oct 10, 2013, time: 14:30

Abstract. A set is porous if arbitrarily close to each point of the set there are holes in the set of radius proportional to their distance away. Porous sets (and their countable unions) give a geometrically interesting class of small sets which have applications in other areas of mathematics.

We discuss two recent applications of porous sets to differentiability problems - generalizations of Rademacher's theorem to Lipschitz functions on infinite dimensional Banach spaces and differentiability of Lipschitz functions inside Lebesgue null subsets of Euclidean spaces.