The visibility problem for Ahlfors regular sets

Abstract

The visibility conjecture states that if $E$ is a planar set with Hausdorff dimension greater than 1, then for almost every direction the “visible part of $E$” (the subset of E that we “see” looking from that direction) has dimension 1. This conjecture is wide open even for self-similar sets with nice separation conditions. I will talk about a recent result where I showed that for Ahlfors regular sets dimension drop occurs for their visible parts.

Damian Dąbrowski

Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.