Title

A Counterexample in the Classification of Open Riemann Surfaces

Publication Type

Journal Article

Publication Date

1974

Abstract

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

Discipline

Accounting

Publication

Proceedings of the American Mathematical Society

Volume

42

Issue

2

First Page

583-587

ISSN

0002-9939

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