JournalsrlmVol. 32, No. 1pp. 135–147

Contracting properties of bounded holomorphic functions

  • Manabu Ito

    Osaka, Japan
Contracting properties of bounded holomorphic functions cover
Download PDF

A subscription is required to access this article.

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. In this article, we formulate a more general contracting property of a bounded holomorphic function in settings with respect to a conformal semimetric. During the study, it will become clear that a proper holomorphic mapping plays a significant role, and that a global result implies a local result. We conclude with a theorem for higher-dimensional spaces.

Cite this article

Manabu Ito, Contracting properties of bounded holomorphic functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 1, pp. 135–147

DOI 10.4171/RLM/930