Favard length and quantitative rectifiability

Abstract

Favard length of a planar set is the average length of its orthogonal projections. The Besicovitch projection theorem, which is one of the cornerstones of geometric measure theory, states the following: if a set E of finite length has positive Favard length, then there exists a rectifiable curve intersecting E in a set of positive length. In this talk I will discuss my recent quantification of this classical result, and its application to Vitushkin’s conjecture.

Damian Dąbrowski

Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.