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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.


Growth and monotonicity properties for elliptically schlicht functions
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by Galatia Cleanthous and Athanasios G. Georgiadis
Conform. Geom. Dyn. 20 (2016), 116-127
Published electronically: May 4, 2016


Let $f$ be a holomorphic function of the unit disc $\mathbb {D},$ with $f(\mathbb {D})\subset \mathbb {D}$ and $f(0)=0$. Littlewood’s generalization of Schwarz’s lemma asserts that for every $w\in f(\mathbb {D}),$ we have $|w|\leq \prod _{j}|z_{j}|,$ where $\{z_{j}\}_j$ are the pre-images of $w.$ We consider elliptically schlicht functions and we prove an analogous bound involving the elliptic capacity of the image. For these functions, we also study monotonicity theorems involving the elliptic radius and elliptic diameter.
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Bibliographic Information
  • Galatia Cleanthous
  • Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
  • MR Author ID: 1032084
  • Email:
  • Athanasios G. Georgiadis
  • Affiliation: Department of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7G, 9220 Aalborg East, Denmark
  • MR Author ID: 911967
  • Email:
  • Received by editor(s): September 30, 2014
  • Received by editor(s) in revised form: February 15, 2016
  • Published electronically: May 4, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 20 (2016), 116-127
  • MSC (2010): Primary 30C80, 30C85, 31A15
  • DOI:
  • MathSciNet review: 3493301