Favard length and quantitative rectifiability

Abstract

Favard length of a set is the average length of its orthogonal projections. The Besicovitch projection theorem states the following: for any set E of finite length whose Favard length is positive there exists a rectifiable curve intersecting E in a set of positive length. The Favard length problem consists of quantifying this theorem, which is crucial for understanding the relation between Favard length and analytic capacity. In this talk I will discuss recent resolution to the Favard length problem for Ahlfors regular sets.

Damian Dąbrowski

Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.