Ideal boundaries of a Riemann surface for the equation

Author:
J. L. Schiff

Journal:
Proc. Amer. Math. Soc. **66** (1977), 57-61

MSC:
Primary 30A50

DOI:
https://doi.org/10.1090/S0002-9939-1977-0450544-9

MathSciNet review:
0450544

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Abstract | References | Similar Articles | Additional Information

Abstract: For a nonnegative density *P* on a hyperbolic Riemann surfaces *R*, let be the subset of the Royden harmonic boundary consisting of the nondensity points of *P*. This ideal boundary, as well as the *P*-harmonic boundary of the *P*-compactification of *R*, have been employed in the study of energy-finite solutions of on *R*. We show that is homeomorphic to , where is the *P*-singular point. It follows that fails to characterize the space in the sense that it is possible for to be homeomorphic to , but is not canonically isomorphic to .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0450544-9

Keywords:
Hyperbolic Riemann surface,
Royden harmonic boundary,
nondensity points,
*P*-harmonic boundary,
*P*-singular point,
canonical isomorphism,
energy-finite solutions of

Article copyright:
© Copyright 1977
American Mathematical Society