Part Metric

A metric defined by

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

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

Explore with Wolfram|Alpha

More things to try:

References

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

Referenced on Wolfram|Alpha

Cite this as:

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

Subject classifications