대한수학회지 (Journal of the Korean Mathematical Society)

  • 제40권3호
  • /
  • Pages.423-434
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  • 2003
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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APPROXIMATION OF NON-HOLOMORPHIC MAPS, AND POLETSKY THEORY OF DISCS

  • 발행 : 2003.05.06
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초록

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.

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참고문헌

  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. https://doi.org/10.1512/iumj.2003.52.2170
  9. H. L. Royden, The Extension of Regular Holomorphic Maps, Proc. Amer. Math. Soc. 43 (1974), 306–310. https://doi.org/10.1090/S0002-9939-1974-0335851-X

피인용 문헌

  1. Local approximation of non-holomorphic discs in almost complex manifolds 2017, https://doi.org/10.1016/j.jmaa.2017.08.050
  2. Lelong functional on almost complex manifolds vol.60, pp.2, 2015, https://doi.org/10.1080/17476933.2014.904297
  3. Poletsky theory of discs in almost complex manifolds vol.59, pp.2, 2014, https://doi.org/10.1080/17476933.2012.734300
  4. Sets of Approximation and Interpolation in ℂ for Manifold-Valued Maps vol.18, pp.3, 2008, https://doi.org/10.1007/s12220-008-9030-2
  5. A Disc Formula for Plurisubharmonic Subextensions in Manifolds vol.25, pp.2, 2015, https://doi.org/10.1007/s12220-014-9474-5