THE VISUAL ANGLE METRIC AND QUASIREGULAR MAPS



: Wang GD, Vuorinen M

Publisher: AMER MATHEMATICAL SOC

: 2016

: Proceedings of the American Mathematical Society

: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

: P AM MATH SOC

: 144

: 11

: 4899

: 4912

: 14

: 0002-9939

DOI: https://doi.org/10.1090/proc/13188


The distortion of distances between points under maps is studied. We first prove a Schwarz-type lemma for quasiregular maps of the unit disk involving the visual angle metric. Then we investigate conversely the quasi-conformality of a bilipschitz map with respect to the visual angle metric on convex domains. For the unit ball or half space, we prove that a bilipschitz map with respect to the visual angle metric is also bilipschitz with respect to the hyperbolic metric. We also obtain various inequalities relating the visual angle metric to other metrics such as the distance ratio metric and the quasihyperbolic metric.



Last updated on 2024-26-11 at 20:53