Displaying similar documents to “Holomorphic approximation of CR functions on tubular submanifolds of ℂ²”

On proper discs in complex manifolds

Barbara Drinovec Drnovšek (2007)

Annales de l’institut Fourier

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Let X be a complex manifold of dimension at least 2 which has an exhaustion function whose Levi form has at each point at least 2 strictly positive eigenvalues. We construct proper holomorphic discs in X through any given point and in any given direction.

Schwarz Reflection Principle, Boundary Regularity and Compactness for J -Complex Curves

Sergey Ivashkovich, Alexandre Sukhov (2010)

Annales de l’institut Fourier

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We establish the Schwarz Reflection Principle for J -complex discs attached to a real analytic J -totally real submanifold of an almost complex manifold with real analytic J . We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in 𝒞 k , α -classes.

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

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We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in ℂ n then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

Some remarks on holomorphic extension in infinite dimensions

Pham Ban (1994)

Colloquium Mathematicae

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In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.