Abstract
If D ⊂ Cn is a region with a smooth boundary and M ⊂ ∂D is a smooth manifold such that for some point p ∈ M the complex linear hull of the tangent plane Tp(M) coincides with Cn, then for each functionf ε A(D) the conditionf¦M=0 implies thatf=0 in D.
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Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 205–212, February, 1974.
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Pinehuk, S.I. A boundary uniqueness theorem for holomorphic functions of several complex variables. Mathematical Notes of the Academy of Sciences of the USSR 15, 116–120 (1974). https://doi.org/10.1007/BF02102390
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DOI: https://doi.org/10.1007/BF02102390