Year: 2025
Type: article
Abstract: A proper subdomain G of the unit disk $$\mathbb {D}$$ D is horocyclically convex (horo-convex) if, for every $$\omega \in \mathbb {D}\cap \partial G$$ ω ∈ D ∩ ∂ G , there exists a horodisk H such that $$\omega \in \partial H$$ ω ∈ ∂ H and $$G\cap H=\emptyset$$ G ∩ H = ∅ . In this paper we give an internal characterization of these domains, namely, that G is horo-convex if and only if any two points can be joined inside G by a $$C^1$$ C 1 curve composed with finitely many Jordan arcs with hyperbolic curvature in $$(-2,2)$$ ( - 2 , 2 ) . We also give a lower bound for the hyperbolic metric of horo-convex regions as well as some of its consequences.
Source: The Journal of Analysis
Authors: Juan Arango, Hugo Arbeláez, Diego Mejía
Institution: Universidad Nacional de Colombia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,090
Funder: Universidad Nacional de Colombia
OpenAlex ID: W4413210427