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    • John Disks, the Apollonian Metric, and Min-Max Properties

      M Huang S Ponnusamy X Wang

      Volume 120 Issue 1 February 2010 pp 83-96

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/120/01/0083-0096

    • Keywords

       

      John disk; Apollonian metric; quasihyperbolic metric; internal distance; min-max property.

    • Abstract

       

      The main results of this paper are characterizations of John disks–the simply connected proper subdomains of the complex plane that satisfy a twisted double cone connectivity property. One of the characterizations of John disks is an analog of a result due to Gehring and Hag who found such a characterization for quasidisks. In both situations the geometric condition is an estimate for the domain’s hyperbolic metric in terms of its Apollonian metric. The other characterization is in terms of an arc min-max property.

    • Author Affiliations

       

      M Huang1 S Ponnusamy2 X Wang1

      1. Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
      2. Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

    • Dates

       
      Published
      February 2010
      Manuscript received
      18 December 2008
      Manuscript revised
      26 October 2009

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