On n-circled -domains of holomorphy
We present various characterizations of n-circled domains of holomorphy with respect to some subspaces of .
On the complex and convex geometry of Ol'shanskii semigroups
To a pair of a Lie group and an open elliptic convex cone in its Lie algebra one associates a complex semigroup which permits an action of by biholomorphic mappings. In the case where is a vector space is a complex reductive group. In this paper we show that such semigroups are always Stein manifolds, that a biinvariant domain is Stein is and only if it is of the form , with convex, that each holomorphic function on extends to the smallest biinvariant Stein domain containing ,...
On the complex geometry of invariant domains in complexified symmetric spaces
Let be a real symmetric space and the corresponding decomposition of the Lie algebra. To each open -invariant domain consisting of real ad-diagonalizable elements, we associate a complex manifold which is a curved analog of a tube domain with base , and we have a natural action of by holomorphic mappings. We show that is a Stein manifold if and only if is convex, that the envelope of holomorphy is schlicht and that -invariant plurisubharmonic functions correspond to convex -invariant...
On the complexification of real-analytic polynomial mappings of ℝ²
We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.
On the continuous extension of holomorphic correspondences
On the -extension and the Hartogs extension
On the domains of existence for plurisubharmonic functions
On the extended tube conjecture.
On the extension in the Hardy classes and the Nevanlinna class
On the extension of holomorphic functions across a real hypersurface.
On the Extension of L2 Holomorphic Functions.
On the extension of L2 holomorphic functions III: negligible weights.
On the Hartogs extension theorem
This paper contains a new approach to a proof of the Hartogs extension theorem and its generalisation. The proof bases only on one complex variable methods.
On the hull of holomorphy of an -manifold in
On the Maximum Modulus Principle for the Tangential Cauchy-Riemann Equations.
On the multiplicative Cousin problem with bounded data
On the Polynomial Convexity of the Union ot Two Maximal Totally Real Subspaces of Cn.
On the regularity of extension to strictly pseudoconvex domains of functions holomorphic in a submanifold in general position
On the removable singularities for meromorphic mappings.
If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.
On the space of the analytic discs which are transversal to a smooth real hypersurface of