location:  Publications → journals → CMB
Abstract view

Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius

Published:2012-01-27
Printed: Jun 2013
• Dimitrios Betsakos,
Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
• Stamatis Pouliasis,
Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
 Format: LaTeX MathJax PDF

Abstract

We prove variants of Schwarz's lemma involving monotonicity properties of condenser capacity and inner radius. Also, we examine when a similar monotonicity property holds for the hyperbolic metric.
 Keywords: condenser capacity, inner radius, hyperbolic metric, Schwarz's lemma
 MSC Classifications: 30C80 - Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination 30F45 - Conformal metrics (hyperbolic, Poincare, distance functions) 31A15 - Potentials and capacity, harmonic measure, extremal length [See also 30C85]