Polynomial hulls and positive currents
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 12 (2003) no. 3, p. 317-334
@article{AFST_2003_6_12_3_317_0,
     author = {Dinh, Tien-Cuong and Lawrence, Mark G.},
     title = {Polynomial hulls and positive currents},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 12},
     number = {3},
     year = {2003},
     pages = {317-334},
     zbl = {1065.32004},
     mrnumber = {2030090},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2003_6_12_3_317_0}
}
Dinh, Tien-Cuong; Lawrence, Mark G. Polynomial hulls and positive currents. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 12 (2003) no. 3, pp. 317-334. http://www.numdam.org/item/AFST_2003_6_12_3_317_0/

[1] Alessandrini ( L.) AND Bassanelli (G.). - Positive ∂∂-closed currents and non-Kähler geometry, J. Geometric Analysis 2, p. 291-316 (1992). | MR 1170477 | Zbl 0735.32008

[2] Alessandrini ( L.) AND Bassanelli (G.). - Plurisubharmonic currents and their extension across analytic subsets, Forum Math. 5, p. 577-602 (1993). | MR 1242890 | Zbl 0784.32014

[3] Alessandrini ( L.) AND Bassanelli (G.). - Lelong numbers of positive plurisubharmonic currents, Results in Mathematics 30, p. 191-224 (1996). | MR 1419939 | Zbl 0870.32002

[4] Alexander ( H.). - Polynomial approximation and hulls in sets of finite linear measure in Cn, Amer. J. Math. 93, p. 65-74 (1971). | MR 284617 | Zbl 0221.32011

[5] Alexander ( H.). - The polynomial hull of a set of finite linear measure in Cn, J. Analyse Math. 47, p. 238-242 (1986). | MR 874052 | Zbl 0615.32009

[6] Alexander ( H.). - Holomorphic chains and the support hypothesis conjecture, J. Am. Math. Soc. 10, No.1, p. 123-138 (1997). | MR 1388871 | Zbl 0870.32003

[7] Alexander ( H. ) AND Wermer (J.). - Linking numbers and boundaries of varieties, Ann. Math. (2) 151, No.1, p. 125-150 (2000). | MR 1745016 | Zbl 1013.32007

[8] Bassanelli ( G.). - A cut-off theorem for plurisubharmonic currents, Forum Math. 6, p. 567-595 (1994). | MR 1295153 | Zbl 0808.32010

[9] Berndtsson ( B.) AND Sibony (N.). - The ∂ equation on a positive current, Inv. math. 147, p. 371-428 (2002). | MR 1881924 | Zbl 1031.32005

[10] Bishop (E. ). - Analyticity in certain Banach algebras , Trans. Amer. Math. Soc., 102, p. 507-544 (1962). | MR 142015 | Zbl 0112.07301

[11] Dinh (T.C. ). - Enveloppe polynomiale d'un compact de longueur finie et chaînes holomorphes à bord rectifiable, Acta Math. 180, No.1, p. 31-67 (1998). | MR 1618329 | Zbl 0942.32008

[12] Dinh (T.C. ). - Orthogonal measures on the boundary of a Riemann surface and polynomial hull of compacts of finite length, J. Funct. Anal. 157, No.2, p. 624-649 (1998). | MR 1638265 | Zbl 0951.32005

[13] Demailly ( J.P.). - Formules de Jensen en plusieurs variables et application arithmétique, Bull. Soc. Math. France 110, p. 75-102 (1982). | Numdam | MR 662130 | Zbl 0493.32003

[14] Dolbeault ( P.) AND Henkin (G.). - Chaînes holomorphes de bord donné dans CPn, Bull. Soc. Math. de France 125, p. 383-445 (1997). | Numdam | MR 1605457 | Zbl 0942.32007

[15] Duval (J. ) AND Sibony (N.). - Polynomial convexity, rational convexity, and currents, Duke Math. J. 79, No.2, p. 487-513 (1995). | MR 1344768 | Zbl 0838.32006

[16] Federer ( H. ). - Geometric Measures theory, NewYork , Springer Verlag, (1969 ). | Zbl 0176.00801

[17] Fornæss (J.) AND Sibony (N.). - Oka's inequality for currents and applications, Math. Ann. 301, p. 399-419 (1995). | MR 1324517 | Zbl 0832.32010

[18] Forstneric ( F.). - The length of a set in the sphere whose polynomial hull contains the origin, Indag. Mathem., N.S. 3 (2), p. 169-172 (1992). | MR 1168343 | Zbl 0762.32007

[19] Garnett ( L.). - Foliations, the ergodic theorem and Brownian motion, J. Funct. Anal. 51, no. 3, p. 285-311 (1983). | MR 703080 | Zbl 0524.58026

[20] Ghys (E.). - Laminations par surfaces de Riemann, Panorama & Synthèses 8, p. 49-95 (1999). | Zbl 1018.37028

[21] Harvey (R. ) AND Lawson (B.). - On boundaries of complex analytic varieties I, Ann. of Math., II. Ser., 102, p. 223-290 (1975). | MR 425173 | Zbl 0317.32017

[22] Harvey (R. ) AND Shiffman (B.). - A characterization of holomorphic chains, Ann. Math. 99, p. 553-587 (1974). | MR 355095 | Zbl 0287.32008

[23] Kallin (E. ). - Fat polynomially convex sets, function Algebras, Proceeding of an International Symposium on Function algebras , Tulane 1965 , Scott, Foresman and Company, p. 149-152 (1966). | MR 194618 | Zbl 0142.10104

[24] King (J.). - The currents defined by analytic varieties, Acta Math. 127, p. 185-220 (1971). | MR 393550 | Zbl 0224.32008

[25] Lawrence ( M.G.). - Polynomial hulls of rectifiable curves , Amer. J. Math. 117, p. 405-417 (1995). | MR 1323682 | Zbl 0827.32012

[26] Lawrence ( M.G. ). - Polynomial hull of sets of finite length in strictly convex domain, Manuscript (1997).

[27] Marinescu ( G. ) AND Dinh (T.C.). - Compactification of hyperconcave ends and theorems of Siu-Yau and Nadel, Preprint, (2002).

[28] Mattila ( P. ). - Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, ( 1975). | MR 1333890

[29] Sarkis (F. ). - CR-meromorphic extension and the nonembeddability of the Andreotti-Rossi CR structure in the projective space, Internat. J. Math. 10, no. 7, p. 897-915 (1999). | MR 1728127 | Zbl 01629322

[30] Shiffman ( B.). - Complete characterization of holomorphic chains of codimension one, Math. Ann 274, p. 233-256 (1986). | MR 838467 | Zbl 0572.32005

[31] Sibony (N. ). - Quelques problèmes de prolongement de courants en analyse complexe, Duke Math. J. 52, p. 157-197 (1985). | MR 791297 | Zbl 0578.32023

[32] Siu (Y.T. ). - Analyticity of Sets Associated to Lelong Numbers and the Extension of Closed Positive Currents, Inventiones math. 27, p. 53-156 (1974). | MR 352516 | Zbl 0289.32003

[33] Skoda (H. ). - Sous-ensemble analytique d'ordre fini ou infini dans Cn, Bull. Soc. math. France 100, p. 353-408 (1972). | Numdam | MR 352517 | Zbl 0246.32009

[34] Skoda (H. ). - Prolongement des courants positifs, fermés de masse finie , Inv. Math. 27, p. 53-156 (1974).

[35] Stolzenberg ( G.). - Uniform approximation on smooth curves , Acta Math. 115, 185-198 (1966). | MR 192080 | Zbl 0143.30005

[36] Takorodo ( M.). - Sur les ensembles pseudoconcaves généraux, J. Math. Soc. Japan 17, no. 3, p. 281-290 (1965). | MR 183901 | Zbl 0147.07403

[37] Wermer (J. ). - The hull of a curve in Cn, Ann. of Math. 68, p. 550-561 (1958). | MR 100102 | Zbl 0084.33402

[38] Ziemer (W.P. ). - Weakly Differentiable Functions, Springer-Verlag, (1989). | MR 1014685 | Zbl 0692.46022