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Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in $ℝ^{n} \subset ℂ^{n}$ .

A Precise Result on the Boundary Regularity of Biholomorphic Mappings.

László Lempert (1986)

Mathematische Zeitschrift

Analycity of CR Equivalences Between Some Real Hypersurfaces in ...n with Degenerate Levi Forms.

C.K. Han (1983)

Inventiones mathematicae

Analytic disks with boundaries in a maximal real submanifold of $𝐂^{2}$

Franc Forstneric (1987)

Annales de l'institut Fourier

Let $M$ be a two dimensional totally real submanifold of class $C^{2}$ in $C^{2}$ . A continuous map $F : \overline{Δ} \to C^{2}$ of the closed unit disk $\overline{Δ} \subset C$ into $C^{2}$ that is holomorphic on the open disk $Δ$ and maps its boundary $b Δ$ into $M$ is called an analytic disk with boundary in $M$ . Given an initial immersed analytic disk $F^{0}$ with boundary in $M$ , we describe the existence and behavior of analytic disks near $F^{0}$ with boundaries in small perturbations of $M$ in terms of the homology class of the closed curve $F^{0} (b Δ)$ in $M$ . We also prove a regularity theorem...

Approximation of biholomorphic mappings by automorphisms of Cn (Erratum).

Jean-Pierre Rosay, Franc Forsternic (1994)

Inventiones mathematicae

Approximation of biholomorphic mappings by automorphisms of Cn.

Jean-Pierre Rosay, Franc Forstneric (1993)

Inventiones mathematicae

Automorphism groups of minimal real-analytic CR manifolds

Robert Juhlin, Bernhard Lamel (2013)

Journal of the European Mathematical Society

We show that the local automorphism group of a minimal real-analytic CR manifold $M$ is a finite dimensional Lie group if (and only if) $M$ is holomorphically nondegenerate by constructing a jet parametrization.

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