Hyperbolic Lambert quadrilaterals and quasiconformal mappings
In this paper under review, the authors give upper bounds for the product and the sum of distances between the opposite sides of a hyperbolic Lambert quadrilateral. Here, a hyperbolic Lambert quadrilateral is a quadrilateral in the hyperbolic plane with three right interior angles. The bounds are all sharp in the sense that there exist some examples only for which the equalities hold. From these, similar bounds are obtained for ideal hyperbolic quadrilaterals. Also, for the images of such quadrilaterals under quasi-conformal mappings, the same expressions are studied.
scientific article; zbMATH DE number 6225479