English

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.

Keywords

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

R2 v1 2026-07-01T04:10:26.035Z