A Characterization of Complex Manifolds Biholomorphic to a Circular Domain.
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 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 remark on separate holomorphy
Let X be a Riemann domain over . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set such that every slice of X with a∉ P is a region of holomorphy with respect to the family .
An infinite-harmonic analogue of a Lelong theorem and infinite-harmonicity cells.
Analytic continuation and regular classes in locally convex Hausdorff spaces
Application of the logarithmic differential to the holomorphic extension problem for -hyperfunctions.
Balanced domains of holomorphy of type
Bergman completeness of complete circular domains
∂̅-cohomology and geometry of the boundary of pseudoconvex domains
In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained how Hartogs...
Composition operators: to the Bloch space to
Let ,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and are Möbius invariant, but is not. We characterize, in function-theoretic terms, when the composition operator induced by an analytic self-map ϕ of the unit disk defines an operator , , which is bounded resp. compact.
Counterexamples to the Gleason problem
Cousin-I spaces and domains of holomorphy
We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.
Domains of biregularity in Clifford analysis
E. E. Levi convexity and the Hans Lewy problem. Part II : vanishing theorems
Espaces de Stein et faisceaux localement libres.
Existence domains for holomorphic Lp functions.
If Ω is a domain of holomorphy in Cn, having a compact topological closure into another domain of holomorphy U ⊂ Cn such that (Ω,U) is a Runge pair, we construct a function F holomorphic in Ω which is singular at every boundary point of Ω and such that F is in Lp(Ω), for any p ∈ (0, +∞).
Fortsetzung von kohärenten analytischen Modulgarben.
Geometric regularity versus analytic regularity higher codimensional case
Geometry of nuclear spaces. II - Linear topological invariants