Hyperbolic metrics on open subsets of Ptolemaic spaces with sharp parameter bounds

Katz, Neil

doi:10.1090/proc/15288

Hyperbolic metrics on open subsets of Ptolemaic spaces with sharp parameter bounds
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by Neil N. Katz PDF

Proc. Amer. Math. Soc. 149 (2021), 2213-2220 Request permission

Abstract:

It is shown that a construction of Z. Zhang and Y. Xiao on open subsets of Ptolemaic spaces yields, when the subset has boundary containing at least two points, metrics that are Gromov hyperbolic with parameter $\log 2$ and strongly hyperbolic with parameter $1$ with no further conditions on the open set. A class of examples is constructed on Hadamard manifolds showing that these estimates of the parameters are sharp.

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