Abstract
Favard length of a planar compact set is the average length of its orthogonal projections. It has been known for a long time that given a nice enough self-similar set of dimension 1, such as the classical 4-corners Cantor set, its Favard length is zero. Consequently, the Favard length of delta-neighbourhoods of such sets converges to 0 as delta goes to 0. The “Favard length problem”, first posed by Peres and Solomyak in 2002, asks about the rate of convergence. The original motivation comes from the Vitushkin’s conjecture in complex analysis. In this talk I will describe a recent solution of this problem for a class of non-homogeneous random Cantor sets. Based on joint work with Alan Chang and Giacomo Del Nin.
Damian Dąbrowski
Assistant professor
My research interests include geometric measure theory and harmonic analysis.