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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Hyperbolic geometric versions of Schwarz’s lemma
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by Dimitrios Betsakos
Conform. Geom. Dyn. 17 (2013), 119-132
Published electronically: November 1, 2013


Let $f$ be a holomorphic self-map of the unit disk $\mathbb {D}$. We prove monotonicity theorems which involve the hyperbolic area, the hyperbolic capacity, and the hyperbolic diameter of the images under $f$ of hyperbolic disks in $\mathbb {D}$. These theorems lead to distortion and modulus growth theorems that generalize the classical lemma of Schwarz and to geometric estimates for the density of the hyperbolic metric.
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Bibliographic Information
  • Dimitrios Betsakos
  • Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
  • MR Author ID: 618946
  • Email:
  • Received by editor(s): June 20, 2013
  • Received by editor(s) in revised form: September 14, 2013
  • Published electronically: November 1, 2013
  • © Copyright 2013 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 17 (2013), 119-132
  • MSC (2010): Primary 30C80, 30C85, 30F45, 30H05
  • DOI:
  • MathSciNet review: 3126908