-closed extension of CR-forms with singularities on a generic manifold.
A boundary cross theorem for separately holomorphic functions
Let D ⊂ ℂⁿ and be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this result to N-fold...
A Characterization of Complex Manifolds Biholomorphic to a Circular Domain.
A correction to and a remark on our paper "Remarks on the proof of a generalized Hartogs Lemma" (Ann. Polon. Math. 70 (1998), 43-47)
A differential geometric characterization of invariant domains of holomorphy
Let be a complex reductive group. We give a description both of domains and plurisubharmonic functions, which are invariant by the compact group, , acting on by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space . Such an invariant domain with a smooth boundary is Stein if and only if the corresponding domain is geodesically convex and the sectional curvature of its boundary fulfills the condition . The term is explicitly computable...
A domain whose envelope of holomorphy is not a domain
We construct a domain of holomorphy in , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in .
A Formula for Interpolation and Division in Cn.
A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces
Using recent development in Poletsky theory of discs, we prove the following result: Let be two complex manifolds, let be a complex analytic space which possesses the Hartogs extension property, let (resp. ) be a non locally pluripolar subset of (resp. ). We show that every separately holomorphic mapping extends to a holomorphic mapping on such that ...
A generalization of the Malgrange-Zerner theorem
A generalized complex Hopf Lemma and its applications to CR mappings.
A Hartogs type extension theorem for generalized (N,k)-crosses with pluripolar singularities
The aim of this paper is to present an extension theorem for (N,k)-crosses with pluripolar singularities.
A lemma on mixed derivatives with applications to edge-of-the-wedge, Radon transformation and a theorem of Forelli
A microlocal version of Cartan-Grauert's theorem
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 .
A new proof of a theorem of Grauert and Remmert by L2-Methods.
A Note Concerning Radó's Theorem.
A note on composition operators on spaces of real analytic functions
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.
A note on Liouville analytic spaces
A note on pluripolar extensions of univalent functions.
A note on the extension of analytic functions off real analytic subsets.
Let X be a closed analytic subset of an open subset Omega of Rn. We look at the problem of extending functions from X to Omega.
A Precise Result on the Boundary Regularity of Biholomorphic Mappings.