Bounded holomorphic functions on negatively curved Kähler manifolds of dimension $\ge 3$

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.

Professor Gabor Szekelyhidi pointed out a mistake in chapter 3 of the paper. The paper has been withdrawn