2025/10/13 by Allu, Vasudevarao, Jose, Alan P
#30L05 #53C23 #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2510.11114
In a recent paper, Zhou, Ponnusamy, and Rasila [Math. Nachr. (2025)] have established that the conformal deformations, with parameter ε>0, of a Gromov hyperbolic space via Busemann functions are uniform spaces for sufficiently small ε. In this paper, we demonstrate that if two proper, roughly starlike Gromov hyperbolic spaces are roughly isometric, then the uniformity of their conformal deformations is a simultaneous property; that is, either both are uniform spaces or neither is. Our results provide a counterpart to the work of Shanmugalingam and Lindquist [Ann. Fenn. Math. (2021)].