The average scale-invariant Cassinian metric is sharply comparable to four standard hyperbolic-type metrics, and its balls in punctured Euclidean space are convex exactly for radius at most log 3.
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On the average scale-invariant Cassinian metric
The average scale-invariant Cassinian metric is sharply comparable to four standard hyperbolic-type metrics, and its balls in punctured Euclidean space are convex exactly for radius at most log 3.