381 research outputs found
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
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