-minimal solutions of on open Riemann surfaces

Author:
Wellington H. Ow

Journal:
Proc. Amer. Math. Soc. **37** (1973), 85-91

MSC:
Primary 30A48

DOI:
https://doi.org/10.1090/S0002-9939-1973-0310233-4

MathSciNet review:
0310233

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Abstract | References | Similar Articles | Additional Information

Abstract: By means of the Royden compactification of an open Riemann surface *R* necessary and sufficient conditions are given for a Dirichlet-finite solution of to be *PD*-minimal on *R*. A relation between *PD*-minimal solutions and *HD*-minimal solutions is obtained. In addition it is shown that the dimension of the space of *PD*-solutions is the same as the number of *P*-energy nondensity points in the finite dimensional case.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0310233-4

Keywords:
Royden harmonic boundary,
*P*-energy nondensity point,
harmonic projection,
*PD*-minimal function,
*HD*-minimal function,
Riesz decomposition

Article copyright:
© Copyright 1973
American Mathematical Society