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Part Metric


A metric defined by

 d(z,w)=sup{|ln[(u(z))/(u(w))]|:u in H^+},

where H^+ denotes the positive harmonic functions on a domain. The part metric is invariant under conformal maps for any domain.


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References

Bear, H. S. "Part Metric and Hyperbolic Metric." Amer. Math. Monthly 98, 109-123, 1991.

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Part Metric

Cite this as:

Weisstein, Eric W. "Part Metric." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PartMetric.html

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