Summary
This paper is a survey of recent developments in the theory of the extension of analytic sets and closed, positive currents.
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Bibliographie
H.ALEXANDER. Continuing 1dimensional analytic sets. Math. Annalen, 191, 1970, p. 14.
J. BECKER. Continuing analytic sets across IRn. Math. Annalen, 195, 1972, 103–106.
E. BEDFORD and B. A. TAYLOR. A new capacity for plurisubharmonic functions. Acta Math., 149, 1982, 1–39.
E. BISHOP. Conditions for the analyticity of certain sets. Michigan Math. Jour., 11, 1964, p. 289–304.
J.P.DEMAILLY. Courants positifs extrémaux et conjecture de Hodge. Inventiones Mathematicae, 69, 1982, 347–374.
J.P.DEMAILLY. Propagation des singularités des courants, positifs, fermés. Arkiv für Mathematik, 1983.
K. DIEDERICH and J.E. FORNAESS. Smooth but not complexanalytic pluripolar sets. Manuscripta Mathematica, 37, 1982, p. 121–125.
H.EL MIR. Sur le prolongement des courants,positifs,fermés. Thèse d’Etat sou tenue à l’Université de Paris VI en Novembre 1982.
H.EL MIR. Sur le prolongement des courants,positifs,fermés. Acta Mathematica, 153, 1984, p. 1–45.
H.FEDERER. Geometric Measure Theory. Springer Berlin, Heidelberg, NewYork, 1969.
P.GRIFFITHS. Two theorems on extension of holomorphic mappings. Inventiones Math., 14, 1971, 27–62.
R. HARVEY. Removable singularities for positive currents. Amer. Jour. of Math., 96, 1974, 67–68.
R.HARVEY. Holomorphic chains and their boundaries. Proceeding of Symposia in Pure Mathematics. Several complex variables, Williamstown, 1975, Vol. 30, 1977, 309–382.
R. HARVEY and J. R.KING. On the structure of positive currents. Invent. Math. 15, 1972, p. 47–52.
R. HARVEY and J. POLKING. Extending analytic objects. Comm. pure and applied Math., 28, 1975, 701–727.
J. KING. The currents defined by analytic varieties. Acta Math. 127, 1971, p. 185–220.
P.LELONG. Intégration sur un ensemble analytique complexe. Bull. Soc. Math. France, 85, 1957, p. 239–262.
P.LELONG. Fonctions entières ( n variables) et fonctions plurisousharmoniques d’ordre fini dans Iç. Jour. Anal. Math. Jérusalem, 12, 1964, p. 365–407.
P.LELONG., Fonctions plurisousharmoniques et formes différentielles positives. Gordon and Breach, Dunod, Paris, Londres, NewYork, 1968.
B.SHIFFMAN. On the continuation of analytic sets. Math. Ann. 185, 1970, 1–12.
N.SIBONY. Quelques problèmes de prolongement de courants en analyse complexe. Préprint Université d’Orsay, 1984, à paraître au Duke Math. Jour.,1984.
Y.T. SIU. Analyticity of Sets associated to Lelong Numbers and the extension of closed positive currents. Inventiones Math., 27, 1974, p. 53–156.
H.SIU. Extension of meromorphic maps into Kahler manifolds. Annals of Mathematics, 102, 1975, 421–462.
H.SKODA. Prolongement des courants, positifs, fermés, de masse finie, Inventiones Mathematicae, 66, 1982, p. 361–376.
W.STOLL. Uber die Fortsetzbarkeit analytischer Mengen endlichen Oberflächeninhaltes. Archiv der Mathematik, 9, 1958, 167–175.
W.STOLL. The growth of the area of a transcendental analytic set I and II. Math. Annalen, t. 156, 1964, p. 47–48 et 144–170.
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© 1986 Springer Fachmedien Wiesbaden
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Skoda, H. (1986). Extension Problems and Positive Currents in Complex Analysis. In: Howard, A., Wong, PM. (eds) Contributions to Several Complex Variables. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06816-7_14
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DOI: https://doi.org/10.1007/978-3-663-06816-7_14
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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