Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Complex Manifolds

Ed. by Fino, Anna Maria

CiteScore 2017: 0.39

SCImago Journal Rank (SJR) 2017: 0.260
Source Normalized Impact per Paper (SNIP) 2017: 0.660

Mathematical Citation Quotient (MCQ) 2017: 0.18

Open Access
See all formats and pricing
More options …

Non compact boundaries of complex analytic varieties in Hilbert spaces

Samuele Mongodi
  • Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56123 Pisa, Italy
  • Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della ricerca scientifica 1, I-00133 Roma, Italy
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Alberto Saracco
  • Corresponding author
  • Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-07-17 | DOI: https://doi.org/10.2478/coma-2014-0002


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.

Keywords: Boundary problem; convexity; maximally complex submanifold; complex Hilbert spaces; CRgeometry


  • [1] L. Ambrosio, B. Kirchheim, Currents in metric spaces, Acta Math., 185 1 (2000), 1–80. Google Scholar

  • [2] L. Ambrosio, B. Kirchheim, Rectifiable sets in metric and Banach spaces, Math. Ann., 318 3 (2000), 527–555. Google Scholar

  • [3] V. Aurich, Bounded analytic sets in Banach spaces, Ann. Inst. Fourier, 36 4 (1986), 229–243. CrossrefGoogle Scholar

  • [4] G. Della Sala, Geometric properties of non-compact CR manifolds, Tesi 14, Edizioni della Normale, Pisa (2009), 103+xv. Google Scholar

  • [5] G. Della Sala, A. Saracco, Non-compact boundaries of complex analytic varieties, Int. J. Math. 18 2 (2007), 203–218. CrossrefWeb of ScienceGoogle Scholar

  • [6] G. Della Sala, A. Saracco, Semi-global extension of maximally complex submanifolds, Bull. Aust. Math. Soc. 84 (2011), 458–474. Web of ScienceGoogle Scholar

  • [7] T.-C. Dinh, Conjecture de Globevnik-Stout et théorème de Morera pur une chaîne holomorphe, Ann. Fac. Sci. Toulouse Math. 8 (1999) 235–257. Google Scholar

  • [8] P. Dolbeault, G. Henkin, Surfaces de Riemann de bord donné dans CPn, in Contributions to complex analysis and analytic geometry, Aspects Math. (Vieweg, Braunschweig, 1994), pp. 163–187. Google Scholar

  • [9] P. Dolbeault, G. Henkin, Chaînes holomorphes de bord donné dans CPn, Bull. Soc. Math. France 125 (1997) 383–445. Google Scholar

  • [10] M. P. Gambaryan, Regularity condition for complex films, Uspekhi Mat. Nauk 40 (1985) 203–204. Google Scholar

  • [11] F. R. Harvey, H. B. Lawson Jr., On boundaries of complex analytic varieties. I, Ann. of Math. (2) 102 (1975), 223–290. Google Scholar

  • [12] F. R. Harvey, H. B. Lawson, Jr., On boundaries of complex analytic varieties. II, Ann. of Math. 106 (1977) 213–238. Google Scholar

  • [13] F. R. Harvey, H. B. Lawson, Jr., Addendum to Theorem 10.4 in “Boundaries of analytic varieties”, Google Scholar

  • [arXiv: math.CV/0002195] (2000). Google Scholar

  • [14] H. Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math. 64 (1956) 514–522. Google Scholar

  • [15] S. Mongodi, Some applications of metric currents to complex analysis, Man. Math. 141 (2013) 363–390. Google Scholar

  • [16] S. Mongodi, Positive metric currents and holomorphic chains in Hilbert spaces, Google Scholar

  • [arXiv:1207.5244], to appear in Rev. Mat. Iberoam. 31 (2015). Google Scholar

  • [17] G. Ruget, A propos des cycles analytiques de dimension infinie, Inv. Math. 8 (1969) 267–312. Google Scholar

  • [18] A. Saracco, Extension problems in complex and CR-geometry, Tesi 9, Edizioni della Normale, Pisa (2008), 153+xiv. Google Scholar

  • [19] G. Stolzenberg, Uniform approximation on smooth curves, Acta Math. 115 (1966) 185–198. Google Scholar

  • [20] J. Wermer, The hull of a curve in Cn, Ann. of Math. 68 (1958) 550–561. Google Scholar

  • [21] R. Williamson, L. Janos, Constructing metrics with the Heine-Borel property, Proc. A.M.S. 100 3 (1987), 567–573. Google Scholar

About the article

Received: 2014-01-10

Accepted: 2014-05-26

Published Online: 2014-07-17

Citation Information: Complex Manifolds, Volume 1, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.2478/coma-2014-0002.

Export Citation

© 2014 Samuele Mongodi and Alberto Saracco. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in