Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets

Gerd Dethloff[1]; Tran Van Tan[1]

  • [1] Université de Bretagne Occidentale, UFR Sciences et Techniques, Département de Mathématiques, 6, avenue Le Gorgeu, BP 452, 29275 Brest Cedex (France).

Annales de la faculté des sciences de Toulouse Mathématiques (2006)

  • Volume: 15, Issue: 2, page 217-242
  • ISSN: 0240-2963

Abstract

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In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ℂ m into ℂ P n with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.

How to cite

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Dethloff, Gerd, and Tan, Tran Van. "Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets." Annales de la faculté des sciences de Toulouse Mathématiques 15.2 (2006): 217-242. <http://eudml.org/doc/10047>.

@article{Dethloff2006,
abstract = {In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of $\{\mathbb\{C\}\}^\{m\}$ into $\{\mathbb\{C\}\}P^\{n\}$ with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.},
affiliation = {Université de Bretagne Occidentale, UFR Sciences et Techniques, Département de Mathématiques, 6, avenue Le Gorgeu, BP 452, 29275 Brest Cedex (France).; Université de Bretagne Occidentale, UFR Sciences et Techniques, Département de Mathématiques, 6, avenue Le Gorgeu, BP 452, 29275 Brest Cedex (France).},
author = {Dethloff, Gerd, Tan, Tran Van},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Nevanlinna theory; uniqueness theorem; moving target},
language = {eng},
number = {2},
pages = {217-242},
publisher = {Université Paul Sabatier, Toulouse},
title = {Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets},
url = {http://eudml.org/doc/10047},
volume = {15},
year = {2006},
}

TY - JOUR
AU - Dethloff, Gerd
AU - Tan, Tran Van
TI - Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2006
PB - Université Paul Sabatier, Toulouse
VL - 15
IS - 2
SP - 217
EP - 242
AB - In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ${\mathbb{C}}^{m}$ into ${\mathbb{C}}P^{n}$ with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.
LA - eng
KW - Nevanlinna theory; uniqueness theorem; moving target
UR - http://eudml.org/doc/10047
ER -

References

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  1. G. Dethloff, Tran Van Tan, Uniqueness problem for meromorphic mappings with truncated multiplicities and moving targets, (2004) Zbl1111.32016
  2. G. Dethloff, Tran Van Tan, An extension of uniqueness theorems for meromorphic mappings, (2004) Zbl1170.32004
  3. H. Fujimoto, The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J. 58 (1975), 1-23 Zbl0313.32005MR393586
  4. H. Fujimoto, Uniqueness problem with truncated multiplicities in value distribution theory, Nagoya Math. J. 152 (1998), 131-152 Zbl0937.32010MR1659377
  5. H. Fujimoto, Uniqueness problem with truncated multiplicities in value distribution theory, II, Nagoya Math. J. 155 (1999), 161-188 Zbl0946.32008MR1711367
  6. S. Ji, Uniqueness problem without multiplicities in value distribution theory, Pacific J. Math. 135 (1988), 323-348 Zbl0629.32022MR968616
  7. D. Q. Manh, Unique range sets for holomorphic curves, Acta Math. Vietnam 27 (2002), 343-348 Zbl1049.32021MR1979813
  8. R. Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta. Math. 48 (1926), 367-391 Zbl52.0323.03
  9. M. Ru, W. Stoll, The Second Main Theorem for moving targets, J. Geom. Anal. 1 (1991), 99-138 Zbl0732.30025MR1113373
  10. M. Ru, A uniqueness theorem with moving targets without counting multiplicity, Proc. Amer. Math. Soc. 129 (2002), 2701-2707 Zbl0977.32013MR1838794
  11. L. Smiley, Geometric conditions for unicity of holomorphic curves, Contemp. Math. 25 (1983), 149-154 Zbl0571.32002MR730045
  12. Z.-H. Tu, Uniqueness problem of meromorphic mappings in several complex variables for moving targets, Tohoku Math. J. 54 (2002), 567-579 Zbl1027.32017MR1936268
  13. W. Yao, Two meromorphic functions sharing five small functions in the sense E ¯ ( k ) ( β , f ) = E ¯ ( k ) ( β , g ) , Nagoya Math. J. 167 (2002), 35-54 Zbl1032.30022MR1924718

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