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Part Metric

A Metric defined by

d(z,w)=\sup\left[{\left\vert{\ln u(z)\over u(w)}\right\vert: u\in H^+}\right],

where $H^+$ denotes the Positive Harmonic Functions on a Domain. The part metric is invariant under Conformal Maps for any Domain.


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

© 1996-9 Eric W. Weisstein