Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A counterexample in the classification of open Riemann surfaces

Author: Young K. Kwon
Journal: Proc. Amer. Math. Soc. 42 (1974), 583-587
MSC: Primary 30A48
MathSciNet review: 0330446
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An HD-function (harmonic and Dirichlet-finite) $ \omega $ on a Riemann surface R is called HD-minimal if $ \omega > 0$ and every HD-function $ \omega '$ with $ 0 \leqq \omega ' \leqq \omega $ reduces to a constant multiple of $ \omega $. An $ H{D^ \sim }$-function is the limit of a decreasing sequence of positive HD-functions and $ H{D^\sim}$-minimality is defined as in HD-functions. The purpose of the present note is to answer in the affirmative the open question: Does there exist a Riemann surface which carries an $ HD^\sim $-minimal function but no HD-minimal functions?

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A48

Retrieve articles in all journals with MSC: 30A48

Additional Information

PII: S 0002-9939(1974)0330446-6
Keywords: HD-function, HD-minimal functions, $ HD^\sim$-function, $ HD^\sim$-minimal function, Dirichlet integral, Royden's compactification, Wiener's compactification, harmonic boundary, harmonic kernel, Riemannian n-manifold
Article copyright: © Copyright 1974 American Mathematical Society