Abstract
It is shown that all invariant metrics and functions on a bounded \({\mathcal{C}^2}\) -smooth domain coincide on an open non-empty subset. The existence of Lempert–Burns–Krantz discs in \({\mathcal{C}^2}\) -smooth domains and other possible applications are also discussed.
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The work is partially supported by the grant of the Polish National Science Centre no. UMO-2011/03/B/ST1/04758.
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Kosiński, Ł. Comparison of invariant functions and metrics. Arch. Math. 102, 271–281 (2014). https://doi.org/10.1007/s00013-013-0596-y
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DOI: https://doi.org/10.1007/s00013-013-0596-y