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Bounded holomorphic functions on negatively curved K\'ahler manifolds of dimension $\ge 3$
- Publication Year :
- 2015
-
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.<br />Comment: Professor Gabor Szekelyhidi pointed out a mistake in chapter 3 of the paper. The paper has been withdrawn
- Subjects :
- Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1512.00368
- Document Type :
- Working Paper