Atoms on the Royden boundary

Kwang-nan Chow and Moses Glasner

Vol. 49 (1973), No. 2, 339–347

DOI: 10.2140/pjm.1973.49.339

Abstract

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 Δ_p of the Royden harmonic boundary are PE-minimal. Points in Δ_P 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

Milestones

Received: 4 August 1972

Published: 1 December 1973