Advanced search
Publication Cover
Complex Variables and Elliptic Equations
An International Journal
Volume 60, 2015 - Issue 2
Submit an article Journal homepage
93
Views
0
CrossRef citations to date
0
Altmetric
Articles

Lelong functional on almost complex manifolds

Barbara Drinovec DrnovšekFaculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000Ljubljana, Slovenia.;Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000Ljubljana, Slovenia.
&
Uroš KuzmanFaculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000Ljubljana, Slovenia.;Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000Ljubljana, Slovenia.Correspondence[email protected]
Pages 168-180 | Received 19 Nov 2013, Accepted 06 Mar 2014, Published online: 22 Apr 2014

References

  • Poletsky EA. Holomorphic currents. Indiana Univ. Math. J. 1993;42:85–144.
  • Lárusson F, Sigurdsson R. Plurisubharmonic functions and analytic discs on manifolds. J. Reine Angew. Math. 1998;501:1–39.
  • Rosay J-P. Poletsky theory of disks on holomorphic manifolds. Indiana Univ. Math. J. 2003;52:157–169.
  • Rosay J-P. Approximation of non-holomorphic maps, and Poletsky theory of discs. J. Korean Math. Soc. 2003;40:423–434.
  • Lárusson F, Sigurdsson R. Plurisubharmonicity of envelopes of disc functionals on manifolds. J. Reine Angew. Math. 2003;555:27–38.
  • Drinovec Drnovšek B, Forstnerič F. Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties. Ann. Polon. Math. 2012;106:171–191.
  • Sukhov A, Tumanov A. Deformations and transversality of pseudo holomorphic discs. J. d’Analyse Math. 2012;116:1–16.
  • Sukhov A, Tumanov A. Filling hypersurfaces by discs in almost complex manifolds of dimension~2. Indiana Univ. Math. J. 2008;57:509–544.
  • Sukhov A, Tumanov A. Regularization of almost complex structures and gluing holomorphic discs to tori. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2011;5:389–411.
  • Ivashkovich S, Shevchisin V. Complex curves in almost-complex manifolds and meromorphic hulls, PhD thesis. Inst. für Math. Ruhr-Universitæt Bochum; 1999.
  • Vekua IN. Generalized analytic functions. Pergamon Press, Addison-Wesley Publishing Co., Inc: London-Paris-Frankfurt, Reading (MA); 1962.
  • Sikorav JC. Some properties of holomorphic curves in almost complex manifolds. In: Audin M, Lafontane J, editors. Holomorphic curves in Symplectic geometry. Basel: Birkhauser; 1994. p. 165–189.
  • Bojarski B. Theory of a generalized analytic vector. Ann. Pol. Math. 1966;17:281–320. Russian.
  • Drinovec Drnovšek B. Discs in Stein manifolds containing given discrete sets. Math. Z. 2002;239:683–702.
  • McDuff D. Singularities and positivity of J-holomorphic curves. In: Audin M, Lafontane J, editors. Holomorphic curves in Symplectic geometry. Basel: Birkhauser; 1994. p. 191–215.
  • Coupet B, Sukhov A, Tumanov A. Proper J-holomorphic discs in Stein domains of dimension 2. Amer. J. Math. 2009;131:653–674.
  • Poletsky EA. Plurisubharmonic functions as solutions of variational problems. Several complex variables and complex geometry, part 1 (Santa Cruz (CA), 1989). Proc. Sympos. Pure Math., Vol. 52, Part 1, Amer. Math. Soc. Providence (RI); 1991. p. 163–171.
  • Bu SQ, Schachermayer W. Approximation of Jensen measures by image measures under holomorphic functions and applications. Trans. Amer. Math. Soc. 1992;331:585–608.
  • Drinovec Drnovšek B, Forstnerič F. The Poletsky-Rosay theorem on singular complex spaces. Indiana Univ. Math. J. 2012;61:1407–1423.
  • Kuzman U. Poletsky theory of discs in almost complex manifolds. Complex Var. Elliptic Equ. 2014;59:262–270.
  • Edigarian A. On definitions of pluricomplex Green function. Ann. Polon. Math. 1997;67:233–246.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.