Research Collection School Of Accountancy

Title

A Counterexample in the Classification of Open Riemann Surfaces

Journal Article

1974

Abstract

An HD-function (harmonic and Dirichlet-finite) Ï‰ on a Riemann surface R is called HD-minimal if $\omega > 0$ and every HD-function Ï‰' with 0 â‰¤ Ï‰' â‰¤ Ï‰ reduces to a constant multiple of Ï‰. An HDâˆ¼-function is the limit of a decreasing sequence of positive HD-functions and HDâˆ¼-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 HDâˆ¼-minimal function but no HD-minimal functions?

Accounting

Publication

Proceedings of the American Mathematical Society

42

2

583-587

ISSN

0002-9939

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