The hyperbolic metric and spherically convex regions
type: Item
instance of: scholarly article
title: The hyperbolic metric and spherically convex regions
zbMATH Open document ID: 1008.30027
author: Seong-A. Kim
author: D. Minda
published in: Journal of Mathematics of Kyoto University
publication date: 2003-04-01T00:00:00Z
review text: It is known that convex regions \(\Omega\subset\mathbb{C}\) can be characterized in terms of the density \(\lambda_{\Omega}(w)\) of the hyperbolic metric \(\lambda_{\Omega}(w)|dw|\). In this paper, the authors derive analogous characterizations for spherically convex regions \(\Omega\) of the Riemann sphere in terms of the spherical density \((1+|w|^2)\lambda_{\Omega}(w)\) of the hyperbolic metric. The authors indicate how the characterizations of Euclidean convexity in the plane can be viewed as a limiting case of their results.
Mathematics Subject Classification ID: 30F45
zbMATH DE Number: 1796030
zbMATH Keywords: convex domain
zbMATH Keywords: spherical density
zbMATH Keywords: hyperbolic metric
zbMATH Keywords: convex subdomain
zbMATH Keywords: spherical geodesic
reviewed by: Martin Chuaqui
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250517634
OpenAlex ID: W1601078435
DOI: 10.1215/KJM/1250517634
description: scientific article; zbMATH DE number 1796030