Holomorphic chains

and the support hypothesis conjecture

Author:
H. Alexander

Journal:
J. Amer. Math. Soc. **10** (1997), 123-138

MSC (1991):
Primary 32C30, 32C25

DOI:
https://doi.org/10.1090/S0894-0347-97-00218-X

MathSciNet review:
1388871

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References | Similar Articles | Additional Information

**[A1]**H. Alexander, Polynomial approximation and hulls in sets of finite linear measure in , 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*, 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

Email:
hja@uic.edu

DOI:
https://doi.org/10.1090/S0894-0347-97-00218-X

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