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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Bibliographische Detailangaben
Veröffentlicht in:	The American mathematical monthly 2015-12, Vol.122 (10), p.1001-1002
1. Verfasser:	Peng, Weimin
Format:	Artikel
Sprache:	eng
Schlagworte:	Analytic functions Entire functions Linear algebra Liouville theorem Mathematical constants Mathematical theorems Mathematics Mathematics education Theorems
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	0002-9890 1930-0972
DOI:	10.4169/amer.math.monthly.122.10.1001