Remarks on the Scale-Invariant Cassinian Metric



: Gendi Wang, Xiaoxue Xu, Matti Vuorinen

Publisher: MALAYSIAN MATHEMATICAL SCIENCES SOC

: 2020

: Bulletin of the Malaysian Mathematical Sciences Society

: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY

: B MALAYS MATH SCI SO

: 19

: 0126-6705

: 2180-4206

DOI: https://doi.org/10.1007/s40840-020-01011-9

: https://arxiv.org/abs/1903.09099


We study the geometry of the scale-invariant Cassinian metric and prove sharp comparison inequalities between this metric and the hyperbolic metric in the case when the domain is either the unit ball or the upper half space. We also prove sharp distortion inequalities for the scale-invariant Cassinian metric under Mobius transformations.



Last updated on 2024-26-11 at 22:18