Author:
Liu Hongjun,Yan Fang,Xia Ling
Abstract
<abstract><p>In this paper, we studied the properties of generalized John domains in metric space. We prove that a domain $ D $ is a $ \varphi $-John domain if, and only if, $ D\backslash P $ is a $ \varphi' $-John domain, where $ P $ is a subset of $ D $ containing finitely many points of $ D $. Meanwhile, we also showed that the union of $ \varphi $-John domains is a $ \varphi'' $-John domain in metric space.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference37 articles.
1. A. F. Beardon, The Apollonian metric of a domain in $\mathbb{R}^n$, In: Quasiconformal mappings and analysis, New York: Springer, 1998, 91–108. https://doi.org/10.1007/978-1-4612-0605-7_8
2. A. Beurling, L. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math., 96 (1956), 125–142. https://doi.org/10.1007/BF02392360
3. O. J. Broch, Geometry of John disks, Ph. D. Thesis, NTNU, 2005.
4. S. M. Buckley, D. A. Herron, X. Xie, Metric space inversions, quasihyperbolic diatance, and uniform space, Indiana Univ. Math. J., 57 (2008), 837–890.
5. F. W. Gehring, K. Hag, O. Martio, Quasihyperbolic geodesics in John domains, Mathe. Scand., 65 (1989), 75–92.