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- W2171938507 abstract "In this paper we consider the inner metric of the Apollonian metric from [3]. Some basic features of this metric are that it is Mobius invariant, equals the hyperbolic metric in balls and half-spaces and has a geodesic connecting an arbitrary pair of points (in most domains). We start by defining the Apollonian metric and its inner metric in order to state our main results. The notation used conforms largely to that of [2] and [19], the reader can consult Section 2.1 of this paper, if necessary. We will be considering domains (open connected non-empty sets) G in the Mobius space Rn := Rn ∪ {∞}. The Apollonian metric is defined for x, y ∈ G R by" @default.
- W2171938507 created "2016-06-24" @default.
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- W2171938507 date "2004-01-01" @default.
- W2171938507 modified "2023-10-18" @default.
- W2171938507 title "The Apollonian Inner Metric" @default.
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- W2171938507 doi "https://doi.org/10.4310/cag.2004.v12.n4.a7" @default.
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