Regularity dimensions: quantifying doubling and uniform perfectness
Metric Geometry
2019-11-01 v1 Classical Analysis and ODEs
Abstract
We study the upper and lower regularity dimensions in relation to the notions of doubling and uniformly perfect. These two regularity properties are closely related which is quantified thanks to the regularity dimensions. The regularity dimensions of pushforward measures onto graphs of Brownian motion are calculated, similarly for pushforwards with respect to quasisymmetric homeomorphisms. We finish by introducing an application to Diophantine approximation in the setting of Kleinian groups.
Cite
@article{arxiv.1910.14074,
title = {Regularity dimensions: quantifying doubling and uniform perfectness},
author = {Douglas C. Howroyd},
journal= {arXiv preprint arXiv:1910.14074},
year = {2019}
}
Comments
15 pages, 4 figures