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Balls defined by nonsmooth vector fields and the Poincaré inequality

Annamaria Montanari, Daniele Morbidelli (2004)

Annales de l’institut Fourier

We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.

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 $Ω^{'}$ .

Behavior of invariant metrics near convexifiable boundary points

Nikolai Nikolov (2003)

Czechoslovak Mathematical Journal

The behaviour of the Carathéodory, Kobayashi and Azukawa metrics near convex boundary points of domains in $ℂ^{n}$ is studied.

Behavior of the Carathéodory metric near strictly convex boundary points.

Jarnicki, Marek, Nikolov, Nikolai (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Bergman completeness of Zalcman type domains

Piotr Jucha (2004)

Studia Mathematica

We give an equivalent condition for Bergman completeness of Zalcman type domains. This also solves a problem stated by Pflug.

Big Picard theorems for holomorphic mappings into the complement of $2 n + 1$ moving hypersurfaces in $ℂ P^{n}$ .

Nguyen Thi Thu Hang, Tran Van Tan (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Boundary behaviour of invariant distances and complex geodesics

Marco Abate (1986)

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

In questa Nota viene studiato il comportamento al bordo delle distanze di Carathéodory e Kobayashi in domini fortemente pseudoconvessi di classe $\mathbf{C}^{2}$ . Come applicazione si dimostra che ogni geodetica complessa in tali domini è estendibile al bordo di classe $\mathbf{C}^{0,\frac{1}{2}}$ .