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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
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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 condenser capacity, inner radius, hyperbolic metric, Schwarz's lemma
MSC Classifications: 30C80, 30F45, 31A15 show english descriptions Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination
Conformal metrics (hyperbolic, Poincare, distance functions)
Potentials and capacity, harmonic measure, extremal length [See also 30C85]
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]
 

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