Bounded holomorphic functions on negatively curved Kähler manifolds of dimension ≥ 3

2015/12/01 by Cao, Jianguo, Shaw, Mei-Chi
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.00368

Abstract

Let M be a simply-connected complete Kahler manifold whose sectional curvature is bounded between two negative numbers. In this paper we prove the existence of non-constant bounded holomorphic functions on M if the complex dimension of M is greater or equal to three. Our proof uses bounded plurisubharmonic exhaustion functions, the Cauchy-Riemann equations and uniform Holder estimates for CR functions on geodesic spheres.

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