Cones, rectifiability, and SIOs

Abstract

Let K(x, V, s) be the open cone centred at x, with direction V, and aperture s. It is easy to see that if a set E satisfies for some V and s the condition:
if x belongs to E, then E has an empty intersection with K(x, V, s),
then E is a subset of a Lipschitz graph. To what extent can we weaken the condition above and still get meaningful information about the geometry of E? It depends on what we mean by ``meaningful information'', of course. For example, one could ask for rectifiability of E, or if E contains big pieces of Lipschitz graphs, or if nice singular integral operators are bounded in L^2(E). In the talk I will discuss these three closely related questions.

Damian Dąbrowski

Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.