Hausdorff dimension of limsup sets of isotropic rectangles in Heisenberg groups

TL;DR

This paper derives a formula for the Hausdorff dimension of limsup sets generated by randomly distributed isotropic rectangles in Heisenberg groups, linking geometric measure theory with group structures.

Contribution

It introduces a new formula for Hausdorff dimension of limsup sets in Heisenberg groups based on directed singular value functions, advancing geometric analysis in non-commutative groups.

Findings

Derived a formula for Hausdorff dimension in Heisenberg groups

Connected geometric measure theory with isotropic rectangles

Provided insights into the structure of limsup sets in non-commutative groups

Abstract

A formula for the Hausdorff dimension of typical limsup sets generated by randomly distributed isotropic rectangles in Heisenberg groups is derived in terms of directed singular value functions.