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Generically strongly q -convex complex manifolds

Terrence Napier, Mohan Ramachandran (2001)

Annales de l’institut Fourier

Suppose ϕ is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold X . The main result is that if the real analytic set of points at which ϕ is not strongly q -convex is of dimension at most 2 q + 1 , then almost every sufficiently large sublevel of ϕ is strongly q -convex as a complex manifold. For X of dimension 2 , this is a special case of a theorem of Diederich and Ohsawa. A version for ϕ real analytic with corners is also obtained.

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Terrence Napier, Mohan Ramachandran (0)

Annales de l’institut Fourier

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