On the uniformization of Hartogs domains in and their envelopes of holomorphy
Ewa Ligocka (1998)
Colloquium Mathematicae
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Ewa Ligocka (1998)
Colloquium Mathematicae
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Sergey Ivashkovich, Alexandre Sukhov (2010)
Annales de l’institut Fourier
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We establish the Schwarz Reflection Principle for -complex discs attached to a real analytic -totally real submanifold of an almost complex manifold with real analytic . We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in -classes.
Barbara Drinovec Drnovšek (2007)
Annales de l’institut Fourier
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Let be a complex manifold of dimension at least which has an exhaustion function whose Levi form has at each point at least strictly positive eigenvalues. We construct proper holomorphic discs in through any given point and in any given direction.
Quang Dieu Nguyen, Dau Hoang Hung (2008)
Annales de l’institut Fourier
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Following Sibony, we say that a bounded domain in is -regular if every continuous real valued function on the boundary of can be extended continuously to a plurisubharmonic function on . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work
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 .
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 continuous on the closure of a Cartan domain and a -invariant finite measure on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face depends only on the restriction of to and is equal to the convolution, in , of the latter restriction with some measure on uniquely determined by . In this article, we give an explicit formula for in...