Hyperbolic Lambert Quadrilaterals and Quasiconformal Mappings

We prove sharp bounds for the product and the sum of two hyperbolic distances between the opposite sides of hyperbolic Lambert quadrilaterals in the unit disk. Furthermore, we study the images of Lambert quadrilaterals under quasiconformal mappings from the unit disk onto itself and obtain sharp results in this case, too.Comment: 21 pages, 7 figure

Triangular ratio metric under quasiconformal mappings in sector domains

Hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result describes the behavior of the triangular ratio metric under quasiconformal maps from one sector onto another one.Comment: 14 pages, 1 figur