Holomorphic chains and the support hypothesis conjecture
Author:
H. Alexander
Journal:
J. Amer. Math. Soc. 10 (1997), 123138
MSC (1991):
Primary 32C30, 32C25
MathSciNet review:
1388871
Fulltext PDF Free Access
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 (44 #1841)
 [A2]
H.
Alexander, Ends of varieties, Bull. Soc. Math. France
120 (1992), no. 4, 523–547 (English, with
English and French summaries). MR 1194275
(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 0302935
(46 #2078)
 [B]
Errett
Bishop, Conditions for the analyticity of certain sets,
Michigan Math. J. 11 (1964), 289–304. MR 0168801
(29 #6057)
 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 (46 #9394)
 [F]
H. Federer, Geometric Integration Theory, Springer Verlag, New York, 1969.
 [G]
Theodore
W. Gamelin, Uniform algebras, PrenticeHall, Inc., Englewood
Cliffs, N. J., 1969. MR 0410387
(53 #14137)
 [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
(56 #5929)
 [HL]
F.R. Harvey and H.B.Lawson,Jr., Complex analytic geometry and measure theory, Proc. Sym. Pure Math. 44 (1986), 261274.
 [HS]
Reese
Harvey and Bernard
Shiffman, A characterization of holomorphic chains, Ann. of
Math. (2) 99 (1974), 553–587. MR 0355095
(50 #7572)
 [K]
James
R. King, The currents defined by analytic varieties, Acta
Math. 127 (1971), no. 34, 185–220. MR 0393550
(52 #14359)
 [R]
Walter
Rudin, Function theory in the unit ball of 𝐶ⁿ,
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of
Mathematical Science], vol. 241, SpringerVerlag, New YorkBerlin,
1980. MR
601594 (82i:32002)
 [S]
Bernard
Shiffman, Complete characterization of holomorphic chains of
codimension one, Math. Ann. 274 (1986), no. 2,
233–256. MR
838467 (87h:32022), http://dx.doi.org/10.1007/BF01457072
 [S2]
Bernard
Shiffman, On the removal of singularities of analytic sets,
Michigan Math. J. 15 (1968), 111–120. MR 0224865
(37 #464)
 [W]
John
Wermer, Banach algebras and several complex variables, 2nd
ed., SpringerVerlag, New YorkHeidelberg, 1976. Graduate Texts in
Mathematics, No. 35. MR 0394218
(52 #15021)
 [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),523547. MR 93k:32012
 [ATU]
 H. Alexander, B.A.Taylor and J.L. Ullman, Areas of projections of analytic sets, Invent. Math. 16 (1972), 335341. MR 46:2078
 [B]
 E. Bishop, Conditions for the analyticity of certain sets, Mich. Math. J. 11 (1964), 289304. MR 29:6057
 1.
 [DO]DO A. Davie and B. Øksendal, Peak interpolation for some algebras of analytic functions, Pacific. J. Math. 41 (1972), 8187. MR 46:9394
 [F]
 H. Federer, Geometric Integration Theory, Springer Verlag, New York, 1969.
 [G]
 T. Gamelin, Uniform Algebras, PrenticeHall, Englewood Cliffs,1969. MR 53:14137
 [H]
 R. Harvey, Holomorphic Chains and Their Boundaries, Proc. Sym. Pure Math. 30 (1977), 309382. MR 56:5929
 [HL]
 F.R. Harvey and H.B.Lawson,Jr., Complex analytic geometry and measure theory, Proc. Sym. Pure Math. 44 (1986), 261274.
 [HS]
 R. Harvey and B. Shiffman, A characterization of holomorphic chains, Ann. Math. 99 (1974), 553587. MR 50:7572
 [K]
 J. King, The currents defined by analytic varieties, Acta Math. 127 (1971), 185220. MR 52:14359
 [R]
 W. Rudin, Function Theory in the Unit Ball of , SpringerVerlag, New York, 1980. MR 82i:32002
 [S]
 B. Shiffman, Complete characterization of holomorphic chains of codimension one, Math. Ann. 274 (1986), 233256. MR 87h:32022
 [S2]
 B. Shiffman, On the removal of singularities of analytic sets, Michigan Math. J. 15 (1968), 111120. MR 37:464
 [W]
 J. Wermer, Banach Algebras and Several Complex Variables, Second Edition, SpringerVerlag, 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 606077045
Email:
hja@uic.edu
DOI:
http://dx.doi.org/10.1090/S089403479700218X
PII:
S 08940347(97)00218X
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
