Annales Academić Scientiarum Fennicć
Mathematica
Volumen 38, 2013, 433-453

HYPERBOLIC LAMBERT QUADRILATERALS AND QUASICONFORMAL MAPPINGS

Matti Vuorinen and Gendi Wang

University of Turku, Department of Mathematics and Statistics
FI-20014 Turku, Finland; vuorinen 'at' utu.fi

University of Turku, Department of Mathematics and Statistics
FI-20014 Turku, Finland; genwan 'at' utu.fi

Abstract. 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.

2010 Mathematics Subject Classification: Primary 51M09; Secondary 51M15.

Key words: Hyperbolic quadrilateral, quasiconformal mapping.

Reference to this article: M. Vuorinen and G. Wang: Hyperbolic Lambert quadrilaterals and quasiconformal mappings. Ann. Acad. Sci. Fenn. Math. 38 (2013), 433-453.

Full document as PDF file

doi:10.5186/aasfm.2013.3845