• Decomposition and Removability Properties of John Domains

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019