Hausdorff dimension of limsup sets of rectangles in the Heisenberg group
Fredrik Ekstr\"om, Esa J\"arvenp\"a\"a, Maarit J\"arvenp\"a\"a
TL;DR
This paper calculates the Hausdorff dimension of limsup sets formed by random rectangles in the Heisenberg group using directed singular value functions, advancing understanding of geometric measure theory in this context.
Contribution
It provides a precise formula for the Hausdorff dimension of these sets, linking it to directed singular value functions in the Heisenberg group.
Findings
Hausdorff dimension explicitly computed
Dimension expressed via directed singular value functions
Results applicable to random geometric constructions in the Heisenberg group
Abstract
The almost sure value of the Hausdorff dimension of limsup sets generated by randomly distributed rectangles in the Heisenberg group is computed in terms of directed singular value functions.
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