Analytic mappings of the unit disk with bounded compression
Complex Variables
2025-07-22 v1 Classical Analysis and ODEs
Abstract
In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give several characterizations of such maps involving the behaviour along geodesic rays, Aleksandrov-Clark measures, zero sets and critical sets.
Cite
@article{arxiv.2507.15200,
title = {Analytic mappings of the unit disk with bounded compression},
author = {Oleg Ivrii and Artur Nicolau},
journal= {arXiv preprint arXiv:2507.15200},
year = {2025}
}
Comments
28 pages