A Generalized Liouville Theorem for Entire Functions

作者:Peng, Weimin*
来源:AMERICAN MATHEMATICAL MONTHLY, 2015, 122(10): 1001-1002.
DOI:10.4169/amer.math.monthly.122.10.1001

摘要

Let f : C -> C be a holomorphic function such that f (z) not equal 0 for any z is an element of C. We show that if g = vertical bar f (z)vertical bar(2)dz circle times d (z) over bar 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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