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Hyperbolic distance, λ-Apollonian metric and John disks
Date Issued
01-01-2014
Author(s)
Abstract
In this paper, by using the hyperbolic distance and the λ-Apollonian metric, we establish a sufficient condition for a simply connected proper subdomain D ⊂ 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.
Volume
32