Schwarz-type lemmas for solutions of ∂ ¯ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich[1]; Jean-Pierre Rosay

  • [1] Université Lille I, département de Mathématiques, 59655 Villeneuve d'Ascq Cedex (France), University of Wisconsin, department of Mathematics, Madison WI 53706 (USA)

Annales de l'Institut Fourier (2004)

  • Volume: 54, Issue: 7, page 2387-2435
  • ISSN: 0373-0956

Abstract

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The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

How to cite

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Ivashkovich, Sergey, and Rosay, Jean-Pierre. "Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds." Annales de l'Institut Fourier 54.7 (2004): 2387-2435. <http://eudml.org/doc/116177>.

@article{Ivashkovich2004,
abstract = {The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.},
affiliation = {Université Lille I, département de Mathématiques, 59655 Villeneuve d'Ascq Cedex (France), University of Wisconsin, department of Mathematics, Madison WI 53706 (USA)},
author = {Ivashkovich, Sergey, Rosay, Jean-Pierre},
journal = {Annales de l'Institut Fourier},
keywords = {Kobayashi-Royden pseudo-norm; almost complex manifolds; Schwarz Lemmas; complete hyperbolicity; Schwarz lemmas},
language = {eng},
number = {7},
pages = {2387-2435},
publisher = {Association des Annales de l'Institut Fourier},
title = {Schwarz-type lemmas for solutions of $\bar\{\partial \}$-inequalities and complete hyperbolicity of almost complex manifolds},
url = {http://eudml.org/doc/116177},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Ivashkovich, Sergey
AU - Rosay, Jean-Pierre
TI - Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds
JO - Annales de l'Institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 7
SP - 2387
EP - 2435
AB - The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.
LA - eng
KW - Kobayashi-Royden pseudo-norm; almost complex manifolds; Schwarz Lemmas; complete hyperbolicity; Schwarz lemmas
UR - http://eudml.org/doc/116177
ER -

References

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