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Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisousharmoniques

Jean-Jacques Loeb (1985)

Annales de l'institut Fourier

Soit G C un groupe de Lie complexe et G R une forme réelle fermée de G C . Un couple ( G C , G R ) est dit pseudo-convexe, s’il existe sur G C une fonction régulière, strictement p.s.h., invariante par l’action de G R et d’exhaustion sur G C / G R . On dit que G R est à spectre imaginaire pur, si pour tout X de Lie ( G R ) , les valeurs propres de ad X sont imaginaires pures. Pour G C à radical simplement connexe, cette dernière propriété équivaut à la pseudo-convexité de ( G C , G R ) . Pour ( G C , G R ) pseudo-convexe et sous une hypothèse de sous-groupe discret,...

Almost Properness of Extremal Mappings

Armen Edigarian, Przemysław Kliś (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We give a simple proof of almost properness of any extremal mapping in the sense of Lempert function or in the sense of Kobayashi-Royden pseudometric.

An application of multivariate total positivity to peacocks

Antoine Marie Bogso (2014)

ESAIM: Probability and Statistics

We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of [F. Hirsch, C. Profeta, B. Roynette and M. Yor, Peacocks and associated martingales vol. 3. Bocconi-Springer (2011)], our guiding example is the result of Carr−Ewald−Xiao [P. Carr, C.-O. Ewald and Y. Xiao, Finance Res. Lett. 5 (2008) 162–171]. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in [F....

An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded

Gregor Herbort (2007)

Annales Polonici Mathematici

Let a and m be positive integers such that 2a < m. We show that in the domain D : = z ³ | r ( z ) : = z + | z | ² + | z | 2 m + | z z | 2 a + | z | 2 m < 0 the holomorphic sectional curvature R D ( z ; X ) of the Bergman metric at z in direction X tends to -∞ when z tends to 0 non-tangentially, and the direction X is suitably chosen. It seems that an example with this feature has not been known so far.

Analytic convexity

Aldo Andreotti, Mauro Nacinovich (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in C n with real analytic boundary

Andrea Iannuzzi (1994)

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

It is shown that given a bounded strictly convex domain Ω in C n with real analitic boundary and a point x 0 in Ω , there exists a larger bounded strictly convex domain Ω with real analitic boundary, close as wished to Ω , such that Ω is a ball for the Kobayashi distance of Ω with center x 0 . The result is applied to prove that if Ω is not biholomorphic to the ball then any automorphism of Ω extends to an automorphism of Ω .

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