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Transactions of the American Mathematical Society

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Holomorphic continuation of smooth functions over Levi-flat hypersurfaces


Author: Eric Bedford
Journal: Trans. Amer. Math. Soc. 232 (1977), 323-341
MSC: Primary 32D15; Secondary 32L05
DOI: https://doi.org/10.1090/S0002-9947-1977-0481100-9
MathSciNet review: 0481100
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Abstract: Here we consider the singularities of a Levi-flat real hypersurface S in C that lie in an analytic variety of codimension 2. It is shown that, from the geometric point of view, there are two kinds of singularities, and the type of singularity determines whether S bounds a domain of holomorphy of type $ {A^\infty }$.


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  • [1] K. Diederich and J. E. Fornaess, Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 3279-3280. MR 0390283 (52:11109)
  • [2] -, A strange bounded smooth domain ofhomomorphy, Bull. Amer. Math. Soc. 82 (1976), 74-76. MR 0397019 (53:879)
  • [3] J. J. Kohn, Global regularity for $ \bar \partial $ on weakly pseudo-convex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292. MR 49 #9442. MR 0344703 (49:9442)
  • [4] P. Lelong, Fonctionnelles analytiques et fonctions entières (n variables), Presses Univ. Montréal, Montréal, 1968, p. 31. MR 0466606 (57:6483)
  • [5] P. H. Rabinowitz, A note on topological degree theory for holomorphic maps, Israel J. Math. 16 (1973), 46-52. MR 49 # 10909. MR 0346183 (49:10909)
  • [6] N. Sibony, Prolongement analytiques des fonctions holomorphes bornées, C. R. Acad. Sci. Paris Sér. A 275 (1972), 973-976. MR 47 #7062. MR 0318515 (47:7062)
  • [7] K. Spallek, Differenzierbare und holomorphe Funktionen auf analytischen Mengen, Math. Ann. 161 (1965), 143-162. MR 33 #4328. MR 0196136 (33:4328)
  • [8] V. S. Vladimirov, Methods of the theory of functions of many complex variables, ``Nauka", Moscow, 1964; English transl., Scripta Technica, M.I.T. Press, Cambridge, Mass., 1966. MR 30 #2163; 34 #1551. MR 0201669 (34:1551)
  • [9] H. Whitney, Complex analytic varieties, Addison-Wesley, Reading, Mass., 1972. MR 0387634 (52:8473)
  • [10] C. Rea, Levi-flat submanifolds and holomorphic extensions of foliations, Ann. Scuola Norm. Sup. Pisa 26 (1972), 665-681. MR 0425158 (54:13115)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0481100-9
Article copyright: © Copyright 1977 American Mathematical Society

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