Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 293-300

A HYPERBOLIC-DISTANCE INEQUALITY FOR HOLOMORPHIC MAPS

Argyrios Christodoulou and Ian Short

The Open University, School of Mathematics and Statistics
Milton Keynes, MK7 6AA, United Kingdom; argyrios.christodoulou 'at' open.ac.uk

The Open University, School of Mathematics and Statistics
Milton Keynes, MK7 6AA, United Kingdom; ian.short 'at' open.ac.uk

Abstract. We prove an inequality which quantifies the idea that a holomorphic self-map of the disc that perturbs two points is close to the identity function.

2010 Mathematics Subject Classification: Primary 30F45; Secondary 30C80.

Key words: Hyperbolic metric, holomorphic map, hyperbolic Riemann surface.

Reference to this article: A. Christodoulou and I. Short: A hyperbolic-distance inequality for holomorphic maps. Ann. Acad. Sci. Fenn. Math. 44 (2019), 293-300.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4425