On the Hartogs extension theorem
نویسندگان
چکیده
منابع مشابه
A 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...
متن کاملHartogs 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...
متن کاملGeneralizing Hartogs’ Trichotomy Theorem
The Trichotomy Principle says that a pair of sets A and B either admits a bijection or else precisely one of these sets injects into the other. Hartogs established logical equivalence between the Trichotomy Principle and the Well-Ordering Principle. As ZF suffices to prove the Schröder-Bernstein theorem, the heart of Trichotomy lies in the existence of some injection connecting A and B (in eith...
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.
متن کامل- THEORETICAL PROOF OF HARTOGS ’ EXTENSION THEOREM ON ( n − 1 ) - COMPLETE COMPLEX SPACES
Let X be a connected normal complex space of dimension n ≥ 2 which is (n − 1)-complete, and let π : M → X be a resolution of singularities. By use of Takegoshi’s generalization of the Grauert-Riemenschneider vanishing theorem, we deduce H cpt(M,O) = 0, which in turn implies Hartogs’ extension theorem on X by the ∂-technique of Ehrenpreis.
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2003
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap80-0-19