A new metric associated with the domain boundary
Abstract
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 the inclusion relation of the c metric balls and some related hyperbolic type metric balls in subdomains of Rn. In addition, we study distortion properties of M\"obius transformations with respect to the c metric in the unit ball and the quasiconformality of bilipschitz mappings in c metric.
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