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On nonimbeddability of Hartogs figures into complex manifolds

E. Chirka;  S. Ivashkovich — 2006

Bulletin de la Société Mathématique de France

We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.

A generalization of Radó's theorem

E. M. Chirka — 2003

Annales Polonici Mathematici

If Σ is a compact subset of a domain Ω ⊂ ℂ and the cluster values on ∂Σ of a holomorphic function f in Ω∖Σ, f' ≢ 0, are contained in a compact null-set for the holomorphic Dirichlet class, then f extends holomorphically onto the whole domain Ω.

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