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arXiv · 2507.15200

Analytic mappings of the unit disk with bounded compression

Oleg Ivrii·Artur Nicolau
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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.

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Oleg Ivrii, Artur Nicolau. 2025-07-21. Analytic mappings of the unit disk with bounded compression. https://arxiv.org/abs/2507.15200

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