Is there any known example of an open subset $U\subset\mathbb{H}^n$ with infinite volume admitting (global) Tchebychev coordinates for $n\geq3$?
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1$\begingroup$ Here's an old question that came to mind though I'm not sure if it helps mathoverflow.net/questions/91429/chebyshev-net-in-3d $\endgroup$– j.c.Commented Dec 8, 2017 at 18:55
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$\begingroup$ What's your definition of Tschebyshev coordinates? $\endgroup$– Deane YangCommented Dec 8, 2017 at 22:00
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$\begingroup$ @DeaneYang: By Tschebyshev coordinates I mean a coordinate system whose coordinate vector fields have all unit length everywhere $\endgroup$– Gianni del FioreCommented Dec 9, 2017 at 1:20
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