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    • Decomposition and Removability Properties of John Domains

      M Huang S Ponnusamy X Wang

      Volume 118 Issue 3 August 2008 pp 357-370

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/118/03/0357-0370

    • Keywords

       

      John domain; John domain decomposition property; John disk; uniform domain; hyperbolic and quasihyperbolic metrics; distance condition; removability property.

    • Abstract

       

      In this paper we characterize John domains in terms of John domain decomposition property. In addition, we also show that a domain 𝐷 in $\mathbb{R}^n$ is a John domain if and only if $D\backslash P$ is a John domain, where 𝑃 is a subset of 𝐷 containing finitely many points of 𝐷. The best possibility and an application of the second result are also discussed.

    • 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
      August 2008
      Manuscript received
      14 May 2007
      Manuscript revised
      9 February 2008

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