Envelopes of holomorphy in
Espaces de Stein et faisceaux localement libres.
Extension of Holomorphic Maps into Hermitian Manifolds.
Extension phenomena for holomorphic geometric structures.
Extension theorems of Sakai type for separately holomorphic and meromorphic functions
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
Factorization of uniformly holomorphic functions
Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the...
Families of analytic discs in with boundaries on a prescribed submanifold
Functional calculus and the Gelfand transformation
Group actions and envelopes of holomorphy.
Holomorphic approximation in infinite-dimensional Riemann domains
Holomorphic functions with singularities on algebraic sets.
Holomorphic q-hulls in top degrees.
Holomorph-prävollständige Resträume zu analytischen Mengen in Steinschen Räumen.
Local holomorphic extendability and non-extendability of -functions on smooth boundaries
Locally Determined Envelopes of Holomorphy in C2.
On balanced L²-domains of holomorphy
We show that any bounded balanced domain of holomorphy is an -domain of holomorphy.
On Dolbeault Cohomology and Envelopes of Holomorphy.
On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle
In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every -smooth CR diffeomorphism between two globally minimal real analytic hypersurfaces in () is real analytic at every point...
On holomorphic maps into compact non-Kähler manifolds
We study the extension problem of holomorphic maps of a Hartogs domain with values in a complex manifold . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain of extension for over is contained in a subdomain of . For such manifolds, we define, in this paper, an invariant Hex using the Hausdorff dimensions of the singular sets of ’s and study its properties to deduce informations on the complex structure 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 ,...