A class of nonpositively curved Kahler manifolds biholomorphic to the unit ball in Cn
Abstract
Let (M,g) be a simply connected complete Kahler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in Cn, where dim M = n.
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