On holomorphic continuation of functions along boundary sections

Abstract

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Boundary cross theorem in dimension 1

“…Proof. This is a slightly modified version of the result in [8]. In fact, Imomkulov-Khujamov suppose that f | E×E can be extended continuously onto E × E. But their proof still works under the hypotheses of Theorem 3.5.…”

“…Hence Y ⊂ G. Thus S * a ⊂ M a for all a ∈ A, where S * a is the non-tangential boundary layer of a pseudoconcave set S (see [9, p. 358]). Consequently, by Lemma 6 and 7 from [9] (see also Lemma 7 and 8 in [8]), S is pluripolar (resp. analytic).…”

Extensions of Analytic and Pluriharmonic Functions in Given Directions by the Chirka Method: a Survey

“…In particular, the following theorem holds. Theorem 2.1 (see [10,27]). Let D ⊂ C n−1 be a bounded domain with a smooth boundary, E ⊂ ∂D be a subset with a positive Lebesgue measure, mes 2n−1 E > 0, and…”

Recent developments in the theory of separately holomorphic mappings

“…By using an idea of Jarnicki and Pflug in [25,27], applying the technique of conformal mappings (see the end of Section 7), using the technique of level sets and using the results of Chirka [9], Imomkulov-Khujamov [17] and Imomkulov [18], we obtain the following "measurable" version with singularities of Theorem 3.…”