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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.

Geodesics for convex complex ellipsoids

Marek Jarnicki, Peter Pflug, Rein Zeinstra (1993)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Geometry of hypersurfaces and mapping theorems in Cn.

D., Jr. Burns, S. Shnider (1979)

Commentarii mathematici Helvetici

Geometry of symmetrized ellipsoids.

Zapałowski, Pawel (2008)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Geometry of the Complex Homogeneous Monge-Ampère Equation.

Pit-Mann Wong (1982)

Inventiones mathematicae

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...

Grunsky coefficient inequalities, Caratheodory metric and extremal quasiconformal mappings.

S.L. Krushkal (1989)