A New Metric Associated with the Domain Boundary: A New Metric Associated with the Domain Boundary - Song, Xingchen; Wang, Gendi (Computational methods and function theory, 2025)
In this paper, we introduce a new metric c ~ which is associated with the domain boundary for a Ptolemy space ( X , d ). Moreover, we study inclusion relations of c ~ metric balls and some related hyperbolic type metric balls in subdomains of R n . In addition, we study distortion properties of the c ~ metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the c ~ metric.