منابع مشابه
Hartogs Type Extension Theorems
Let ∆ ⊆ C be the open unit disc and let Σ ⊆ ∆×∆ be a compact set such that K = Σ ∪ (∂∆×∆) is a connected set. It is a classical result by Hartogs that if Σ is an analytic variety over ∆ with the boundary in ∂∆×∆, then every function holomorphic in a connected neighbourhood of K extends holomorphically to a neighbourhood of ∆ × ∆. It is proved that the same conclusion holds if Σ is a ‘continuous...
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We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.
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Let X be a connected normal Stein space of pure dimension d ≥ 2 with isolated singularities only. By solving a weighted ∂-equation with compact support on a desingularization of X , we derive Hartogs’ Extension Theorem on X by the ∂-idea due to Ehrenpreis.
متن کاملSome Remarks on Hartogs’ Extension Lemma
Motivated by a result and a question by E. M. Chirka we consider the Hartogs’ extension property for some connected sets in C2 of the form K = Σ ∪ (∂Δ × Δ), where Σ is a possibly nonconnected compact subset of Δ×Δ ⊂ C2.
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The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces, and regular valuations on coherent so...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2010
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-010-9134-3