Displaying similar documents to “Embedding subsets of tori Properly into 2

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.

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.

Jensen measures and unbounded B - regular domains in C n

Quang Dieu Nguyen, Dau Hoang Hung (2008)

Annales de l’institut Fourier

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Following Sibony, we say that a bounded domain Ω in C n is B -regular if every continuous real valued function on the boundary of Ω can be extended continuously to a plurisubharmonic function on Ω . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in C n . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work

A microlocal version of Cartan-Grauert's theorem

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

Annales Polonici Mathematici

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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 n n .

Holomorphic retractions and boundary Berezin transforms

Jonathan Arazy, Miroslav Engliš, Wilhelm Kaup (2009)

Annales de l’institut Fourier

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In an earlier paper, the first two authors have shown that the convolution of a function f continuous on the closure of a Cartan domain and a K -invariant finite measure μ on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face F depends only on the restriction of f to F and is equal to the convolution, in  F , of the latter restriction with some measure μ F on F uniquely determined by  μ . In this article, we give an explicit formula for μ F in...