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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



An extension of the theorem of Hartogs

Author: L. R. Hunt
Journal: Trans. Amer. Math. Soc. 166 (1972), 491-495
MSC: Primary 32D99; Secondary 57D40
MathSciNet review: 0296341
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Abstract: Hartogs proved that every function which is holomorphic on the boundary of the unit ball in $ {C^n},n > 1$, can be extended to a function holomorphic on the ball itself. It is conjectured that a real k-dimensional $ {\mathcal{C}^\infty }$ compact submanifold of $ {C^n},k > n$, is extendible over a manifold of real dimension $ (k + 1)$. This is known for hypersurfaces (i.e., $ k = 2n - 1$) and submanifolds of real codimension 2. It is the purpose of this paper to prove this conjecture and to show that we actually get C-R extendibility.

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Keywords: Extendibility of holomorphic functions, C-R extendibility, the Levi form
Article copyright: © Copyright 1972 American Mathematical Society