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Continuity of condenser capacity under holomorphic motions

Part of: Two-dimensional theory Complex dynamical systems Geometric function theory

Published online by Cambridge University Press:  29 June 2020

Stamatis Pouliasis
Stamatis Pouliasis*
Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas79409, USA
*
e-mail: stamatis.pouliasis@ttu.edu
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Abstract

We show that condenser capacity varies continuously under holomorphic motions, and the corresponding family of the equilibrium measures of the condensers is continuous with respect to the weak-star convergence. We also study the behavior of uniformly perfect sets under holomorphic motions.

Keywords

Condenser capacityequilibrium measureuniformly perfect setsholomorphic motions

MSC classification

Primary: 31A15: Potentials and capacity, harmonic measure, extremal length 31A05: Harmonic, subharmonic, superharmonic functions 30C85: Capacity and harmonic measure in the complex plane 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 340 - 348
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Copyright
© Canadian Mathematical Society 2020

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