HOLOMORPHIC EXTENSIONS OF MAPS FROM THE BOUNDARY OF KAHLER MANIFOLDS

Abstract

In this note, we show that there exists a unique holomorphic extension of a given map which satisfies the tangential Cauchy-Riemann equation on the hyperconvex boundary of a Käler manifold into a complete Kähler manifold with strongly seminegative curvature, provided there is a plurisubharmonic function on the domain which has at least two positive eigenvalues at some point.