Envelopes of Holomorphy and Polynomial Hulls.
Enveloppes polynomiales de variétés réelles dans C2.
We present here three examples concerning polynomial hulls of some manifolds in C2.1. Some real surfaces with equation w = P (z,z') + G(z) where P is a homogeneous polynomial of degree n and G(z) = o(|z|n) at 0 which are locally polynomially convex at 0.2. Some real surfaces MF with equation w = zn+kz'n + F(z,z') such that the hull of Mf ∩ B'(0,1) contains a neighbourhood of 0.3. A contable union of totally real planes (Pj) such that B'(0,1) ∩ (∪j∈N Pj) is polynomially convex.
Enveloppes polynomiales d’unions de plans réels dans
En reprenant le travail de Weinstock concernant l’union de deux sous-espaces, nous montrons que peut être obtenu comme l’union d’un nombre fini de sous-espaces vectoriels totalement réels maximaux, pour tout supérieur à un. Ceci contraste avec le cas des droites complexes de , dont il faut un ensemble de capacité positive pour que l’enveloppe soit tout l’espace. On étudie aussi le cas des trois plans réels de : si les trois unions deux à deux ne sont pas polynomialement convexes, alors l’enveloppe...
Espaces de Banach-Stein
Espaces de Stein et faisceaux localement libres.
Every finitely presented group is the ...of some two dimensional Stein space.
Every Stein Subvariety Admits a Stein Neighborhood
Evolution of subsets of and parabolic problem for the Levi equation
Existence of open quasiconvex subsets dense in a given space
Explicit imbedding of the (punctured) disc into C2.
Exploding orbits of holomorphic structures.
Extending Families of Pseudoconcave Complex Spaces.
Extending holomorphic mappings from subvarieties in Stein manifolds
Suppose that is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space to is a uniform limit of entire maps . We prove that a holomorphic map from a closed complex subvariety in a Stein manifold admits a holomorphic extension provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.
Extending holomorphic maps in infinite dimensions
Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in...
Extension and Decomposition with Local Boundary Regularity Properties in Pseudoconvex Domains.
Extension of Analytic Functional Calculus Mappings and Duality by ...-Closed Forms with Growth.
Extension of Holomorphic Maps into Hermitian Manifolds.
Extension of Proper Holomorphic Mappings Past the Boundary.
Extensions of Rings of Holomorphic Functions.
Fibrés holomorphes dont la base et la fibre sont des espaces de Stein