Some Remarks on Hartogs’ Extension Lemma
نویسندگان
چکیده
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.
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 کامل$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles
In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains.
متن کاملNotes on well-balanced orientations
This note contains some remarks on the well-balanced orientation theorem of Nash-Williams [10]. He announced in [11] an extension of his theorem. We present a proof for a generalization of this extension. We show some new consequences of Nash-Williams’ odd vertex pairing theorem. A slight generalization of a theorem of Lovász [7] will also be proved.
متن کاملThe disk property. A short survey
We present some results obtained over the years regarding the disk property for complex manifolds and its connections with pseudoconvexity. The idea to use holomorphic disks to study domains of holomorphy in C goes back all the way to F. Hartogs [12] at the beginning of the twentieth century. Hartogs’ result was extended by Osgood [19] who proved what is called ”Hartogs extension theorem” stati...
متن کاملCohomology of Semi 1-coronae and Extension of Analytic Subsets
Contents 1. Introduction and notations 1 2. Remarks on the proofs of theorems in [12] 3 3. An isomorphism theorem for semi 1-coronae 5 3.1. Bump lemma: surjectivity of cohomology 6 3.2. Approximation 8 4. Extension of coherent sheaves and analytic subsets 13 References 15
متن کامل