A Generalized Liouville Theorem for Entire Functions
Let be a holomorphic function such that for any . We show that if is a complete Riemannian metric, then f must be a constant. As a corollary we give a new proof of the classical Liouville theorem.
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| Veröffentlicht in: | The American mathematical monthly 2015-12, Vol.122 (10), p.1001-1002 |
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| container_issue | 10 |
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| container_title | The American mathematical monthly |
| container_volume | 122 |
| creator | Peng, Weimin |
| description | Let be a holomorphic function such that for any . We show that if is a complete Riemannian metric, then f must be a constant. As a corollary we give a new proof of the classical Liouville theorem. |
| doi_str_mv | 10.4169/amer.math.monthly.122.10.1001 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0002-9890 |
| ispartof | The American mathematical monthly, 2015-12, Vol.122 (10), p.1001-1002 |
| issn | 0002-9890 1930-0972 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Alma/SFX Local Collection |
| subjects | Analytic functions Entire functions Linear algebra Liouville theorem Mathematical constants Mathematical theorems Mathematics Mathematics education Theorems |
| title | A Generalized Liouville Theorem for Entire Functions |
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