Removable Singularities for Analytic Varieties in Strongly Pseudoconvex Domains
نویسندگان
چکیده
Let M be a closed maximally complex submanifold of some relatively compact open subset A of the boundary of a strictly pseudoconvex domain Ω of C. We find an open domain à of Ω, depending only on Ω and A, and a complex variety with isolated singularities W ⊂ à such that bW ∩ A = M .
منابع مشابه
Cohomology and Removable Subsets
Let X be a (connected and reduced) complex space. A qcollar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions) hypersurfaces. Finiteness and vanishing cohomology theorems obtained in [17], [18] for semi q-coronae are generalized in this context and lead to results on extension...
متن کاملRemovable singularities for weighted Bergman spaces
We develop a theory of removable singularities for the weighted Bergman space Aμ(Ω) = {f analytic in Ω : R Ω |f | dμ < ∞}, where μ is a Radon measure on C. The set A is weakly removable for Aμ(Ω \ A) if Aμ(Ω \ A) ⊂ Hol(Ω), and strongly removable for Aμ(Ω \A) if Aμ(Ω \A) = Aμ(Ω). The general theory developed is in many ways similar to the theory of removable singularities for Hardy H spaces, BMO...
متن کاملRemovable singularities for Hardy spaces
In this paper we study removable singularities for Hardy spaces of analytic functions on general domains. Two different definitions are given. For compact sets they turn out to be equal and moreover independent of the surrounding domain, as was proved by D. A. Hejhal. For non-compact sets the difference between the definitions is studied. A survey of the present knowledge is given, except for t...
متن کاملComplete Localization of Domains with Noncompact Automorphism Groups
We prove a characterization of the domains in en with an automorphism orbit accumulating at a boundary point at which the boundary is real analytic and convex up to a biholomorphic change of local coordinates. This result generalizes the well-known Wong-Rosay theorem on strongly pseudoconvex domains to the case of locally convex domains with real analytic boundaries.
متن کاملOn Analytic Interpolation Manifolds in Boundaries of Weakly Pseudoconvex Domains
Let Ω be a bounded, weakly pseudoconvex domain in Cn, n ≥ 2, with real-analytic boundary. A real-analytic submanifold M ⊂ ∂Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to O(Ω). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be rel...
متن کامل