Mass transference principle: from balls to arbitrary shapes

2018/12/20 by Koivusalo, Henna, Rams, Michał · 3 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.08557

Abstract

The mass transference principle, proved by Beresnevich and Velani in 2006, is a strong result that gives lower bounds for the Hausdorff dimension of limsup sets of balls. We present a version for limsup sets of open sets of arbitrary shape.

Cited by

• Twisted Diophantine approximation for matrix transformations of tori
• A dimensional mass transference principle from balls to open sets and applications to dynamical Diophantine approximation
• Hitting Probabilities and the Ekström-Persson conjecture

Related

• The Mass Transference Principle: Ten Years On
• A general principle for Hausdorff measure
• Extraction of optimal subsequences of sequence of balls, and application to optimality estimates of mass transference principles
• Mass transference principle from rectangles to rectangles in Diophantine approximation
• A mass transference principle and sets with large intersections