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APPROXIMATION OF NON-HOLOMORPHIC MAPS, AND POLETSKY THEORY OF DISCS
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 Title & Authors
APPROXIMATION OF NON-HOLOMORPHIC MAPS, AND POLETSKY THEORY OF DISCS
Rosay, Jean-Pierre;
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 Abstract
We prove an approximation result, and we get a new proof of the main result in [7]. I hope that this new proof may be a step towards a generalization of the Poletsky theory of discs to the case of almost complex manifolds.
 Keywords
holomorphic discs;complex manifold;
 Language
English
 Cited by
1.
Lelong functional on almost complex manifolds, Complex Variables and Elliptic Equations, 2015, 60, 2, 168  crossref(new windwow)
2.
A Disc Formula for Plurisubharmonic Subextensions in Manifolds, The Journal of Geometric Analysis, 2015, 25, 2, 1401  crossref(new windwow)
3.
Poletsky theory of discs in almost complex manifolds, Complex Variables and Elliptic Equations, 2014, 59, 2, 262  crossref(new windwow)
4.
Sets of Approximation and Interpolation in ℂ for Manifold-Valued Maps, Journal of Geometric Analysis, 2008, 18, 3, 720  crossref(new windwow)
 References
1.
A. Douady, Le problème des modules pour les sous espaces analytiques compact d'un space analytique donné, Ann. Inst. Fourier 16 (1966), 1-95.

2.
B. Berndtsson and J.-P. Rosay, Quasi-Isometric Vector Bundles and Bounded Factorization of Holomorphic Matrices, to appear in Ann. Inst. Fourier.

3.
F. Larusson and R. Sigurdsson, Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math. 501 (1998), 1–39.

4.
F. Larusson and R. Sigurdsson, Plurisubharmonicity of envelopes of disc functionals on manifolds, preprint

5.
A. Edigarian, A note on Rosay's paper, preprint

6.
L. Hormander, An Introduction to Complex Analysis in Several Complex Variables, Van Nostrand, Princeton, 1966.

7.
E. Poletsky, Plurisubharmonic functions as solutions of variational problems, Proc. Symp. Pure Math. 52 (1991), 163–171.

8.
J. P. Rosay, Poletsky theory of disks on holomorphic manifolds, Indiana Univ. Math. J. 52 (2003), 157–170. crossref(new window)

9.
H. L. Royden, The Extension of Regular Holomorphic Maps, Proc. Amer. Math. Soc. 43 (1974), 306–310. crossref(new window)