2024/11/01 by Allu, Vasudevarao, Jose, Alan P · 1 citation
#30F45 #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG) #Primary 30C65 #Secondary 30C20
paper · doi:10.48550/arxiv.2411.00906
The purpose of this paper is to provide a uniformization procedure for Gromov hyperbolic spaces, which need not be geodesic or proper. We prove that the conformal deformation of a Gromov hyperbolic space is a bounded uniform space. Further, we show that there is a natural quasi-isometry between the Gromov boundary and the metric boundary of the deformed space. Our main results are a generalization of the results of Bonk, Heninonen, and Koskela [Proposition 4.5, Proposition 4.13, Astérisque 270 (2001)].