Gareth Speight (Warwick) - "Surfaces meeting porous sets in positive measure"

Abstract

A set is porous if each point of the set sees nearby holes of radius proportional to their distance away. Porous sets are somehow small - they are nowhere dense and have Lebesgue measure zero in finite dimensions. We ask whether typical C¹ surfaces meet porous sets in positive measure and see that the answer depends on the dimension of the surfaces. We then discuss recent results on Frechet differentiability related to surfaces and porous sets.