A Morse-theoretical proof of 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...
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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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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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A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x over a finite alphabet is ultimately periodic if and only if, for some n, the number of different factors of length n appearing in x is less than n+1. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d ≥ 2. A legitimate extensi...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2007
ISSN: 1050-6926,1559-002X
DOI: 10.1007/bf02922095