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Equality case for an elliptic area condenser inequality and a related Schwarz type lemma

Part of: Geometric function theory Two-dimensional theory Real and complex geometry

Published online by Cambridge University Press:  19 August 2019

Georgios Kelgiannis
Georgios Kelgiannis*
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece (gkelgian@math.auth.gr)
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Abstract

We give an equality condition for a symmetrization inequality for condensers proved by F.W. Gehring regarding elliptic areas. We then use this to obtain a monotonicity result involving the elliptic area of the image of a holomorphic function f.

Keywords

condensercapacityconformal mapelliptic areasymmetrization

MSC classification

Primary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Secondary: 30C85: Capacity and harmonic measure in the complex plane 31A15: Potentials and capacity, harmonic measure, extremal length 51M10: Hyperbolic and elliptic geometries (general) and generalizations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 91 - 104
Copyright
Copyright © Edinburgh Mathematical Society 2019

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