# 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.

Date
15 Jun 2020 18:00
Location
University of Minnesota
##### Damian Dąbrowski
###### Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.