Vol. 49, No. 2, 1973

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Atoms on the Royden boundary

Kwang-nan Chow and Moses Glasner

Vol. 49 (1973), No. 2, 339–347

Let R be a hyperbolic Riemann surface and P a nonnegative C1-density on R. Every PE-minimal function is shown to be PD-minimal. Conversely PD-minimal functions corresponding to atoms in a certain subset Δp of the Royden harmonic boundary are PE-minimal. Points in ΔP are atoms with respect to the PD-representing measure if and only if they are atoms with respect to the HD-representing measure.

Mathematical Subject Classification
Primary: 30A50
Received: 4 August 1972
Published: 1 December 1973
Kwang-nan Chow
Moses Glasner