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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.

Grauert's line bundle convexity, reduction and Riemann domains

Viorel Vâjâitu (2016)

Czechoslovak Mathematical Journal

We consider a convexity notion for complex spaces X with respect to a holomorphic line bundle L over X . This definition has been introduced by Grauert and, when L is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if H 0 ( X , L ) separates each point of X , then X can be realized as a Riemann domain over the complex projective space...

Hartogs type extension theorems on some domains in Kähler manifolds

Takeo Ohsawa (2012)

Annales Polonici Mathematici

Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and...

Holomorphic isometries of Cartan domains of type one

Edoardo Vesentini (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Holomorphic isometries for the Kobayashi metric of a class of Cartan domains are characterized.

Holomorphic semigroups of holomorphic isometries

Edoardo Vesentini (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.

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