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Tytuł artykułu

Non compact boundaries of complex analytic varieties in Hilbert spaces

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EN
Abstrakty
EN
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H.We deal with the problem by cutting with a family of complex hyperplanes and applying the already known result for the compact case.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
1
Opis fizyczny
Daty
otrzymano
2014-01-10
zaakceptowano
2014-05-26
online
2014-07-17
Twórcy
  • Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56123 Pisa, Italy, mongodi@mat.uniroma2.it
  • Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della ricerca scientifica 1, I-00133 Roma,
    Italy
  • Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle
    Scienze 53/A, I-43124 Parma, Italy, georges.dloussky@univ-amu.fr
Bibliografia
  • [1] L. Ambrosio, B. Kirchheim, Currents in metric spaces, Acta Math., 185 1 (2000), 1–80.
  • [2] L. Ambrosio, B. Kirchheim, Rectifiable sets in metric and Banach spaces, Math. Ann., 318 3 (2000), 527–555.
  • [3] V. Aurich, Bounded analytic sets in Banach spaces, Ann. Inst. Fourier, 36 4 (1986), 229–243.[Crossref]
  • [4] G. Della Sala, Geometric properties of non-compact CR manifolds, Tesi 14, Edizioni della Normale, Pisa (2009), 103+xv.
  • [5] G. Della Sala, A. Saracco, Non-compact boundaries of complex analytic varieties, Int. J. Math. 18 2 (2007), 203–218.[Crossref][WoS]
  • [6] G. Della Sala, A. Saracco, Semi-global extension of maximally complex submanifolds, Bull. Aust. Math. Soc. 84 (2011),458–474.[WoS]
  • [7] T.-C. Dinh, Conjecture de Globevnik-Stout et théorème de Morera pur une chaîne holomorphe, Ann. Fac. Sci. ToulouseMath. 8 (1999) 235–257.
  • [8] P. Dolbeault, G. Henkin, Surfaces de Riemann de bord donné dans CPn, in Contributions to complex analysis and analyticgeometry, Aspects Math. (Vieweg, Braunschweig, 1994), pp. 163–187.
  • [9] P. Dolbeault, G. Henkin, Chaînes holomorphes de bord donné dans CPn, Bull. Soc. Math. France 125 (1997) 383–445.
  • [10] M. P. Gambaryan, Regularity condition for complex films, Uspekhi Mat. Nauk 40 (1985) 203–204.
  • [11] F. R. Harvey, H. B. Lawson Jr., On boundaries of complex analytic varieties. I, Ann. of Math. (2) 102 (1975), 223–290.
  • [12] F. R. Harvey, H. B. Lawson, Jr., On boundaries of complex analytic varieties. II, Ann. of Math. 106 (1977) 213–238.
  • [13] F. R. Harvey, H. B. Lawson, Jr., Addendum to Theorem 10.4 in “Boundaries of analytic varieties”,
  • [arXiv:math.CV/0002195] (2000).
  • [14] H. Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a relatedtheorem for regular functions of two complex variables, Ann. of Math. 64 (1956) 514–522.
  • [15] S. Mongodi, Some applications of metric currents to complex analysis, Man. Math. 141 (2013) 363–390.
  • [16] S. Mongodi, Positive metric currents and holomorphic chains in Hilbert spaces,
  • [arXiv:1207.5244], to appear in Rev. Mat.Iberoam. 31 (2015).
  • [17] G. Ruget, A propos des cycles analytiques de dimension infinie, Inv. Math. 8 (1969) 267–312.
  • [18] A. Saracco, Extension problems in complex and CR-geometry, Tesi 9, Edizioni della Normale, Pisa (2008), 153+xiv.
  • [19] G. Stolzenberg, Uniform approximation on smooth curves, Acta Math. 115 (1966) 185–198.
  • [20] J. Wermer, The hull of a curve in Cn, Ann. of Math. 68 (1958) 550–561.
  • [21] R. Williamson, L. Janos, Constructing metrics with the Heine-Borel property, Proc. A.M.S. 100 3 (1987), 567–573.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_coma-2014-0002
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