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Holomorphic chains
and the support hypothesis conjecture

Author: H. Alexander
Journal: J. Amer. Math. Soc. 10 (1997), 123-138
MSC (1991): Primary 32C30, 32C25
MathSciNet review: 1388871
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  • [A1] H. Alexander, Polynomial approximation and hulls in sets of finite linear measure in ${\Bbb C}^n$, Amer. J. Math. 93 (1971), 65- 74. MR 44:1841
  • [A2] H. Alexander, Ends of varieties, Bull. Soc. math. France 120 (1992),523-547. MR 93k:32012
  • [ATU] H. Alexander, B.A.Taylor and J.L. Ullman, Areas of projections of analytic sets, Invent. Math. 16 (1972), 335-341. MR 46:2078
  • [B] E. Bishop, Conditions for the analyticity of certain sets, Mich. Math. J. 11 (1964), 289-304. MR 29:6057
  • 1. [DO]DO A. Davie and B. Øksendal, Peak interpolation for some algebras of analytic functions, Pacific. J. Math. 41 (1972), 81-87. MR 46:9394
  • [F] H. Federer, Geometric Integration Theory, Springer- Verlag, New York, 1969.
  • [G] T. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs,1969. MR 53:14137
  • [H] R. Harvey, Holomorphic Chains and Their Boundaries, Proc. Sym. Pure Math. 30 (1977), 309-382. MR 56:5929
  • [HL] F.R. Harvey and H.B.Lawson,Jr., Complex analytic geometry and measure theory, Proc. Sym. Pure Math. 44 (1986), 261-274.
  • [HS] R. Harvey and B. Shiffman, A characterization of holomorphic chains, Ann. Math. 99 (1974), 553-587. MR 50:7572
  • [K] J. King, The currents defined by analytic varieties, Acta Math. 127 (1971), 185-220. MR 52:14359
  • [R] W. Rudin, Function Theory in the Unit Ball of ${\Bbb C}^n$, Springer-Verlag, New York, 1980. MR 82i:32002
  • [S] B. Shiffman, Complete characterization of holomorphic chains of codimension one, Math. Ann. 274 (1986), 233-256. MR 87h:32022
  • [S2] B. Shiffman, On the removal of singularities of analytic sets, Michigan Math. J. 15 (1968), 111-120. MR 37:464
  • [W] J. Wermer, Banach Algebras and Several Complex Variables, Second Edition, Springer-Verlag, New York, 1976. MR 52:15021

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Additional Information

H. Alexander
Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 S Morgan (M/C 249), Chicago, Illinois 60607-7045

Keywords: Holomorphic chains, currents of type $(k, k)$, locally rectifiable currents
Received by editor(s): July 15, 1994
Received by editor(s) in revised form: April 26, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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