Annales Academię Scientiarum Fennicę
Mathematica
Volumen 32, 2007, 371-380
Hunan Normal University, Department of Mathematics
Changsha, Hunan 410081, P.R. China; xtwang 'at' hunnu.edu.cn
Hunan Normal University, Department of Mathematics
Changsha, Hunan 410081, P.R. China
Indian Institute of Technology Madras, Department of Mathematics
Chennai-600 036, India; samy 'at' iitm.ac.in
Huzhou Teachers College, Department of Mathematics
Huzhou, Zhejiang 313000, P.R. China
Abstract. In this paper, by using the hyperbolic distance and the \lambda-Apollonian metric, we establish a sufficient condition for a simply connected proper subdomain D \subset C to be a John disk. We also construct two examples to show that the converse of this result does not necessarily hold. As a consequence the answer to Conjecture 6.2.12 in the Ph.D. thesis of Broch [2] is negative.
2000 Mathematics Subject Classification: Primary 30C65.
Key words: Hyperbolic distance, \lambda-Apollonian metric, John disk.
Reference to this article: X. Wang, M. Huang, S. Ponnusamy and Y. Chu: Hyperbolic distance, \lambda-Apollonian metric and John disks. Ann. Acad. Sci. Fenn. Math. 32 (2007), 371-380.
Full document as PDF file
Copyright © 2007 by Academia Scientiarum Fennica