Some remarks on Hartogs’ extension lemma

Abstract

Motivated by a result and a question by E. M. Chirka we consider the Hartogs’ extension property for some connected sets in C 2 \mathbb {C}^ 2 of the form K = Σ ∪ ( ∂ Δ × Δ ¯ ) K=\Sigma \cup (\partial \Delta \times \overline {\Delta }) , where Σ \Sigma is a possibly nonconnected compact subset of Δ ¯ × Δ ¯ ⊂ C 2 \overline {\Delta }\times \overline {\Delta }\subset \mathbb {C}^ 2 .