Closures of open analytic polyhedra

P. J. de Paepe

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Embeddability of real analytic Cauchy-Riemann manifolds

Aldo Andreotti, Gregory A. Fredricks (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Generically strongly $q$ -convex complex manifolds

Terrence Napier, Mohan Ramachandran (2001)

Annales de l’institut Fourier

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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.