An extension of the theorem of Hartogs
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- by L. R. Hunt PDF
- Trans. Amer. Math. Soc. 166 (1972), 491-495 Request permission
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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 491-495
- MSC: Primary 32D99; Secondary 57D40
- DOI: https://doi.org/10.1090/S0002-9947-1972-0296341-9
- MathSciNet review: 0296341