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Evolution of subsets of $ℂ^{2}$ and parabolic problem for the Levi equation

Zbigniew Slodkowski, Giuseppe Tomassini (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

Some open problems in higher dimensional complex analysis and complex dynamics.

John Erik Fornaess, Nessim Sibony (2001)

Publicacions Matemàtiques

We present a collection of problems in complex analysis and complex dynamics in several variables.

[unknown]

Terrence Napier, Mohan Ramachandran (0)

Annales de l’institut Fourier

Displaying 1 – 4 of 4

Evolution of subsets of ℂ 2 and parabolic problem for the Levi equation

Generically strongly q -convex complex manifolds

Some open problems in higher dimensional complex analysis and complex dynamics.

[unknown]

Currently displaying 1 – 4 of 4

Evolution of subsets of $ℂ^{2}$ and parabolic problem for the Levi equation

Generically strongly $q$ -convex complex manifolds