Generalized Gehring-Osgood, Dovgoshey-Hariri-Vuorinen, Nikolov-Andreev, and Ibragimov metrics on metric spaces are proved Gromov hyperbolic, with improved constants for the Gehring-Osgood and Nikolov-Andreev metrics.
On distortion of quasiregular mappings of the upper half plane
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abstract
We prove a sharp result for the distortion of a hyperbolic type metric under $K$-quasiregular mappings of the upper half plane. The proof makes use of a new kind of Bernoulli inequality and the Schwarz lemma for quasiregular mappings.
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Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity
Generalized Gehring-Osgood, Dovgoshey-Hariri-Vuorinen, Nikolov-Andreev, and Ibragimov metrics on metric spaces are proved Gromov hyperbolic, with improved constants for the Gehring-Osgood and Nikolov-Andreev metrics.