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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Growth and monotonicity properties for elliptically schlicht functions
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by Galatia Cleanthous and Athanasios G. Georgiadis PDF
Conform. Geom. Dyn. 20 (2016), 116-127 Request permission


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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Additional 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