Hartogs extension for generalized tubes in Cn
نویسندگان
چکیده
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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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.
متن کاملA Morse-theoretical Proof of the Hartogs Extension Theorem
100 years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables), whose global counterpart was understood later: holomorphic functions in a connected neighborhood V(∂Ω) of a connected boundary ∂Ω b C (n > 2) do extend holomorphically and uniquely to the domain Ω. Martinelli in the early 1940’s and Ehrenpreis in 1961 obtained a rigorous pro...
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A complex analytic space is said to have the D∗-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X × C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the fun...
متن کاملAnalyzing Generalized Tubes
Many objects in the real world are tubular in shape and this paper is about understanding this object class, which we refer to in the paper as generalized tubes (hereafter GTs). Intuitively, a GT is constructed by sweeping some planar closed curve (the GT cross-section) along a 3D space curve (the GT axis). First, we examine the GT class as a whole and identify two important GT subclasses where...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.01.049