Non compact boundaries of complex analytic varieties in Hilbert spaces

Samuele Mongodi; Alberto Saracco

Complex Manifolds (2014)

  • Volume: 1, Issue: 1, page 34-44, electronic only
  • ISSN: 2300-7443

Abstract

top
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.

How to cite

top

Samuele Mongodi, and Alberto Saracco. "Non compact boundaries of complex analytic varieties in Hilbert spaces." Complex Manifolds 1.1 (2014): 34-44, electronic only. <http://eudml.org/doc/276957>.

@article{SamueleMongodi2014,
abstract = {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.},
author = {Samuele Mongodi, Alberto Saracco},
journal = {Complex Manifolds},
keywords = {Boundary problem; convexity; maximally complex submanifold; complex Hilbert spaces; CRgeometry; boundary problem for complex manifolds; strongly convex subsets of Hilbert spaces},
language = {eng},
number = {1},
pages = {34-44, electronic only},
title = {Non compact boundaries of complex analytic varieties in Hilbert spaces},
url = {http://eudml.org/doc/276957},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Samuele Mongodi
AU - Alberto Saracco
TI - Non compact boundaries of complex analytic varieties in Hilbert spaces
JO - Complex Manifolds
PY - 2014
VL - 1
IS - 1
SP - 34
EP - 44, electronic only
AB - 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.
LA - eng
KW - Boundary problem; convexity; maximally complex submanifold; complex Hilbert spaces; CRgeometry; boundary problem for complex manifolds; strongly convex subsets of Hilbert spaces
UR - http://eudml.org/doc/276957
ER -

References

top
  1. [1] L. Ambrosio, B. Kirchheim, Currents in metric spaces, Acta Math., 185 1 (2000), 1–80. Zbl0984.49025
  2. [2] L. Ambrosio, B. Kirchheim, Rectifiable sets in metric and Banach spaces, Math. Ann., 318 3 (2000), 527–555. Zbl0966.28002
  3. [3] V. Aurich, Bounded analytic sets in Banach spaces, Ann. Inst. Fourier, 36 4 (1986), 229–243. [Crossref] Zbl0591.46005
  4. [4] G. Della Sala, Geometric properties of non-compact CR manifolds, Tesi 14, Edizioni della Normale, Pisa (2009), 103+xv. Zbl1200.32022
  5. [5] G. Della Sala, A. Saracco, Non-compact boundaries of complex analytic varieties, Int. J. Math. 18 2 (2007), 203–218. [Crossref][WoS] Zbl1140.32025
  6. [6] G. Della Sala, A. Saracco, Semi-global extension of maximally complex submanifolds, Bull. Aust. Math. Soc. 84 (2011), 458–474. [WoS] Zbl1239.32028
  7. [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. 
  8. [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. Zbl0821.32008
  9. [9] P. Dolbeault, G. Henkin, Chaînes holomorphes de bord donné dans CPn, Bull. Soc. Math. France 125 (1997) 383–445. 
  10. [10] M. P. Gambaryan, Regularity condition for complex films, Uspekhi Mat. Nauk 40 (1985) 203–204. Zbl0576.32016
  11. [11] F. R. Harvey, H. B. Lawson Jr., On boundaries of complex analytic varieties. I, Ann. of Math. (2) 102 (1975), 223–290. Zbl0317.32017
  12. [12] F. R. Harvey, H. B. Lawson, Jr., On boundaries of complex analytic varieties. II, Ann. of Math. 106 (1977) 213–238. Zbl0361.32010
  13. [13] F. R. Harvey, H. B. Lawson, Jr., Addendum to Theorem 10.4 in “Boundaries of analytic varieties”, 
  14. [arXiv: math.CV/0002195] (2000). 
  15. [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. Zbl0074.06204
  16. [15] S. Mongodi, Some applications of metric currents to complex analysis, Man. Math. 141 (2013) 363–390. Zbl1267.32038
  17. [16] S. Mongodi, Positive metric currents and holomorphic chains in Hilbert spaces, Zbl1332.32015
  18. [arXiv:1207.5244], to appear in Rev. Mat. Iberoam. 31 (2015). 
  19. [17] G. Ruget, A propos des cycles analytiques de dimension infinie, Inv. Math. 8 (1969) 267–312. Zbl0188.25102
  20. [18] A. Saracco, Extension problems in complex and CR-geometry, Tesi 9, Edizioni della Normale, Pisa (2008), 153+xiv. Zbl1165.32001
  21. [19] G. Stolzenberg, Uniform approximation on smooth curves, Acta Math. 115 (1966) 185–198. Zbl0143.30005
  22. [20] J. Wermer, The hull of a curve in Cn, Ann. of Math. 68 (1958) 550–561. Zbl0084.33402
  23. [21] R. Williamson, L. Janos, Constructing metrics with the Heine-Borel property, Proc. A.M.S. 100 3 (1987), 567–573. Zbl0626.54035

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.