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A microlocal version of Cartan-Grauert's theorem

I. V. Maresin, A. G. Sergeev (1998)

Annales Polonici Mathematici

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 n n .

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 : Δ C 2 of the closed unit disk Δ 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...

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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