A Liouville theorem on complete non-K\"ahler manifolds
Yuang Li, Chuanjing Zhang, Xi Zhang
TL;DR
This paper extends Liouville theorems for holomorphic functions from complete K"ahler manifolds to a broader class of complete non-K"ahler Gauduchon manifolds, broadening the understanding of complex analysis in differential geometry.
Contribution
It generalizes Yau's Liouville theorem from K"ahler to non-K"ahler Gauduchon manifolds, providing new insights into holomorphic functions on these spaces.
Findings
Liouville theorem proven for a class of complete Gauduchon manifolds
Extension of Yau's result to non-K"ahler case
Broader understanding of holomorphic functions in complex geometry
Abstract
In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete K\"ahler manifolds to the complete non-K\"ahler case.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows