Ahlfors’ currents in higher dimension

Henry de Thélin[1]

  • [1] Université Paris-Sud (Paris 11) Mathématique, Bât. 425 91405 Orsay France.

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 1, page 121-133
  • ISSN: 0240-2963

Abstract

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We consider a nondegenerate holomorphic map f : V ↦ X where ( X , ω ) is a compact Hermitian manifold of dimension larger than or equal to k and V is an open connected complex manifold of dimension k . In this article we give criteria which permit to construct Ahlfors’ currents in X .

How to cite

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de Thélin, Henry. "Ahlfors’ currents in higher dimension." Annales de la faculté des sciences de Toulouse Mathématiques 19.1 (2010): 121-133. <http://eudml.org/doc/115855>.

@article{deThélin2010,
abstract = {We consider a nondegenerate holomorphic map $f: V \mapsto X$ where $(X, \omega )$ is a compact Hermitian manifold of dimension larger than or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$. In this article we give criteria which permit to construct Ahlfors’ currents in $X$.},
affiliation = {Université Paris-Sud (Paris 11) Mathématique, Bât. 425 91405 Orsay France.},
author = {de Thélin, Henry},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Ahlfors currents; mapping degree},
language = {eng},
month = {1},
number = {1},
pages = {121-133},
publisher = {Université Paul Sabatier, Toulouse},
title = {Ahlfors’ currents in higher dimension},
url = {http://eudml.org/doc/115855},
volume = {19},
year = {2010},
}

TY - JOUR
AU - de Thélin, Henry
TI - Ahlfors’ currents in higher dimension
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/1//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 1
SP - 121
EP - 133
AB - We consider a nondegenerate holomorphic map $f: V \mapsto X$ where $(X, \omega )$ is a compact Hermitian manifold of dimension larger than or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$. In this article we give criteria which permit to construct Ahlfors’ currents in $X$.
LA - eng
KW - Ahlfors currents; mapping degree
UR - http://eudml.org/doc/115855
ER -

References

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  11. Range (R.M.).— Holomorphic functions and integral representations in several complex variables, Springer-Verlag (1986). Zbl0591.32002MR847923
  12. Sibony (N.) and Wong (P.M.).— Some remarks on the Casorati-Weierstrass theorem, Ann. Polon. Math., 39, p. 165-174 (1981). Zbl0476.32005MR617458
  13. Stoll (W.).— A general first main theorem of value distribution, Acta Math., 118, p. 111-191 (1967). Zbl0148.31905MR217339
  14. Wu (H.).— Remarks on the first main theorem in equidistribution theory II, J. Differential Geometry, 2, p. 369-384 (1968). Zbl0177.11301MR276501

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