Inequalities of Schwarz–Pick type with branch points and the pseudo-hyperbolic distance. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Ito, Manabu
• Is Part Of: Complex variables and elliptic equations. Volume 62:Issue 6(2017)
• Page Start: 786
• Page End: 794
• Publication Date: 2017-06-03
• Subjects: Pseudo-hyperbolic distance -- Schwarz–Pick lemma -- branch points; Primary: 30C80 -- 30F45 -- Secondary: 30C25 -- 30H05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2016.1244188
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract: The classical Schwarz–Pick lemma implies that a holomorphic function of the open unit disk into itself gives a contraction with respect to the hyperbolic metric on the disk. As such, differential forms of the Schwarz–Pick lemma have been recently discussed in consideration of branch points of a holomorphic function. We in this article demonstrate that the pseudo-hyperbolic distance, which does not arise from a Riemannian metric, remains suitable for a Schwarz–Pick type of inequality even in more general settings with the existence of branch points.