Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ideal boundaries of a Riemann surface for the equation $ \Delta u=Pu$


Author: J. L. Schiff
Journal: Proc. Amer. Math. Soc. 66 (1977), 57-61
MSC: Primary 30A50
MathSciNet review: 0450544
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a nonnegative density P on a hyperbolic Riemann surfaces R, let $ {\Delta ^P}$ 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 $ {\delta _P}$ of the P-compactification of R, have been employed in the study of energy-finite solutions of $ \Delta u = Pu$ on R. We show that $ {\Delta ^P}$ is homeomorphic to $ {\delta _P} - \{ {s_P}\} $, where $ {s_P}$ is the P-singular point. It follows that $ {\delta _P}$ fails to characterize the space $ PBE(R)$ in the sense that it is possible for $ {\delta _P}$ to be homeomorphic to $ {\delta _Q}$, but $ PBE(R)$ is not canonically isomorphic to $ QBE(R)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A50

Retrieve articles in all journals with MSC: 30A50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0450544-9
PII: S 0002-9939(1977)0450544-9
Keywords: Hyperbolic Riemann surface, Royden harmonic boundary, nondensity points, P-harmonic boundary, P-singular point, canonical isomorphism, energy-finite solutions of $ \Delta u = Pu$
Article copyright: © Copyright 1977 American Mathematical Society