Quadrilaterals and John disks (Q558496)

The author investigates the relations involving ordered quadruples of points on the boundary of a Jordan domain, and shows that these relations hold iff the domain is a John disk. In particular, the author examined the connections between absolute cross ratios and moduli of corresponding quadrilaterals. The author also gives a characterization of John disks based on a relation between diameters of subarcs of the boundary and bounds for moduli of associated quadrilaterals. These results are one sided analogues to characterizations of quasidisks.