Dynamical Resistance Day

Mass transference principle: from balls to arbitrary shapes
04 de Dezembro | 11h00min | Henna Koivusalo (University of Bristol, UK)

Title: Mass transference principle: from balls to arbitrary shapes

Mass transference principles give lower bounds for the Hausdorff dimension and Hausdorff measure of limsup sets. Heuristically speaking, they say the following: if some sequence of sets gives a limsup set of full measure, then the limsup set of sets positioned equivalently to the original sets but smaller, cannot have Hausdorff dimension (or Hausdorff measure) too low. The first mass transference principles were discovered by Jaffard in 2000 and Beresnevich and Velani in 2006. Since then, mass transference principles in various contexts have been found by many. In a joint work with Michal Rams, I proved a mass transference principle for the case where balls with a full measure limsup set are replaced by subsets of arbitrary shape (open subsets of the original balls). In this talk I will present this result and compare to some other recent works.