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Condenser Capacity Under Multivalent Holomorphic Functions

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Abstract

We prove an inequality for the capacity of a condenser via a holomorphic function f, under a valency assumption on f, and we show that equality occurs if and only if f has finite constant valency. Also, we generalize a well known inequality for quasiregular mappings and we give a necessary condition for the case of equality.

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Acknowledgments

The second author wants to thank Dimitrios Betsakos for interesting discussions on the subject.

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Author notes

  1. Stamatis Pouliasis

    Present address: Département de Mathématiqes et de Statistique, Université Laval, Quebec, G1V 0A6, QC, Canada

Authors and Affiliations

  1. Department of Mathematics, University of Crete, Knossos Ave, Iraklio, 71409, Greece

    Michael Papadimitrakis

  2. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 541242, Greece

    Stamatis Pouliasis

Authors
  1. Michael Papadimitrakis
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  2. Stamatis Pouliasis
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Correspondence to Stamatis Pouliasis.

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Communicated by Alexander Solynin.

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Papadimitrakis, M., Pouliasis, S. Condenser Capacity Under Multivalent Holomorphic Functions. Comput. Methods Funct. Theory 13, 11–20 (2013). https://doi.org/10.1007/s40315-012-0004-9

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  • DOI: https://doi.org/10.1007/s40315-012-0004-9

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