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Displaying similar documents to “Boundaries of graphs of harmonic functions.”

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

Similarity:

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

Similarity:

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.