Computational Methods and Function Theory 4 (2004), No. 2, 419--434
Copyright Heldermann Verlag 2004
Ole Jacob Broch
olejacb@math.ntnu.no , Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Relations involving ordered quadruples of points on the boundary of a Jordan domain are investigated, and it is shown that these relations hold if and only if the domain is a John disk. In particular connections between absolute cross ratios and moduli of corresponding quadrilaterals are examined. A characterization of John disks based on a relation between diameters of subarcs of the boundary and bounds for moduli of associated quadrilaterals is also given. The results are one sided analogues to characterizations of quasidisks.
Keywords: John disk, quadrilateral, reversed triangle inequality, cross ratio, quasimöbius map, modulus, harmonic doubling condition.
MSC 2000: Primary 30C20; Secondary 30C99.
[FullText-pdf (276 K)] [FullText-ps (519 K)]