Spherical convexity and hyperbolic metric

Research output: Contribution to journalArticlepeer-review

Abstract

Let Ω be a domain in C with hyperbolic metric λΩ(z) | dz| with Gaussian curvature - 4. Mejía and Minda proved in their 1990 paper that Ω is (Euclidean) convex if and only if d(z, ∂Ω) λΩ(z) ≥ 1 / 2 for z∈ Ω , where d(z, ∂Ω) denotes the Euclidean distance from z to the boundary ∂Ω. In the present note, we will provide similar characterizations of spherically convex domains in terms of the spherical density of the hyperbolic metric.

Original languageEnglish
Pages (from-to)167-175
Number of pages9
JournalJournal of Analysis
Volume24
Issue number1
DOIs
Publication statusPublished - 2016 Jun

Keywords

  • Hyperbolic metric
  • Spherically convex
  • Tree

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics
  • Geometry and Topology

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