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The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds
It is proved that if is a weakly 1-complete Kähler manifold with only one end, then or there exists a proper holomorphic mapping of onto a Riemann surface.
Observations on harmonic maps and singular varieties
Generically strongly -convex complex manifolds
Suppose is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold . The main result is that if the real analytic set of points at which is not strongly -convex is of dimension at most , then almost every sufficiently large sublevel of is strongly -convex as a complex manifold. For of dimension , this is a special case of a theorem of Diederich and Ohsawa. A version for real analytic with corners is also obtained.
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