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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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
1974
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| Online Access: | https://ink.library.smu.edu.sg/soa_research/668 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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? |
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