A counterexample in the classification of open Riemann surfaces
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- by Young K. Kwon
- Proc. Amer. Math. Soc. 42 (1974), 583-587
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330446-6
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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
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 583-587
- MSC: Primary 30A48
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330446-6
- MathSciNet review: 0330446