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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References | Similar Articles | Additional Information

**[A1]**H. Alexander,*Polynomial approximation and hulls in sets of finite linear measure in Cn*, Amer. J. Math.**93**(1971), 65–74. MR**0284617****[A2]**H. Alexander,*Ends of varieties*, Bull. Soc. Math. France**120**(1992), no. 4, 523–547 (English, with English and French summaries). MR**1194275****[ATU]**H. Alexander, B. A. Taylor, and J. L. Ullman,*Areas of projections of analytic sets*, Invent. Math.**16**(1972), 335–341. MR**0302935****[B]**Errett Bishop,*Conditions for the analyticity of certain sets*, Michigan Math. J.**11**(1964), 289–304. MR**0168801****1.**A. M. Davie and B. K. Øksendal,*Peak interpolation sets for some algebras of analytic functions*, Pacific J. Math.**41**(1972), 81–87. MR**0310293****[F]**H. Federer,*Geometric Integration Theory*, Springer- Verlag, New York, 1969.**[G]**Theodore W. Gamelin,*Uniform algebras*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR**0410387****[H]**Reese Harvey,*Holomorphic chains and their boundaries*, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 1, Williams Coll., Williamstown, Mass., 1975) Amer. Math. Soc., Providence, R. I., 1977, pp. 309–382. MR**0447619****[HL]**F.R. Harvey and H.B.Lawson,Jr., Complex analytic geometry and measure theory, Proc. Sym. Pure Math. 44 (1986), 261-274.**[HS]**Reese Harvey and Bernard Shiffman,*A characterization of holomorphic chains*, Ann. of Math. (2)**99**(1974), 553–587. MR**0355095****[K]**James R. King,*The currents defined by analytic varieties*, Acta Math.**127**(1971), no. 3-4, 185–220. MR**0393550****[R]**Walter Rudin,*Function theory in the unit ball of 𝐶ⁿ*, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR**601594****[S]**Bernard Shiffman,*Complete characterization of holomorphic chains of codimension one*, Math. Ann.**274**(1986), no. 2, 233–256. MR**838467**, 10.1007/BF01457072**[S2]**Bernard Shiffman,*On the removal of singularities of analytic sets*, Michigan Math. J.**15**(1968), 111–120. MR**0224865****[W]**John Wermer,*Banach algebras and several complex variables*, 2nd ed., Springer-Verlag, New York-Heidelberg, 1976. Graduate Texts in Mathematics, No. 35. MR**0394218**

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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