A Counterexample in the Classification of Open Riemann Surfaces
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∼-...
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1974
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sg-smu-ink.soa_research-16672010-09-22T14:12:03Z A Counterexample in the Classification of Open Riemann Surfaces Kwon, Young Koan 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? 1974-01-01T08:00:00Z text https://ink.library.smu.edu.sg/soa_research/668 info:doi/10.1090/S0002-9939-1974-0330446-6 Research Collection School Of Accountancy eng Institutional Knowledge at Singapore Management University Accounting |
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Accounting Kwon, Young Koan A Counterexample in the Classification of Open Riemann Surfaces |
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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? |
| format |
text |
| author |
Kwon, Young Koan |
| author_facet |
Kwon, Young Koan |
| author_sort |
Kwon, Young Koan |
| title |
A Counterexample in the Classification of Open Riemann Surfaces |
| title_short |
A Counterexample in the Classification of Open Riemann Surfaces |
| title_full |
A Counterexample in the Classification of Open Riemann Surfaces |
| title_fullStr |
A Counterexample in the Classification of Open Riemann Surfaces |
| title_full_unstemmed |
A Counterexample in the Classification of Open Riemann Surfaces |
| title_sort |
counterexample in the classification of open riemann surfaces |
| publisher |
Institutional Knowledge at Singapore Management University |
| publishDate |
1974 |
| url |
https://ink.library.smu.edu.sg/soa_research/668 |
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