[Déformation de grands disques pseudo-holomorphes et application à la pseudonorme de Hanh]
Nous simplifions la preuve du théorème montrant que près de tout disque pseudo-holomorphe il passe un disque pseudo-holomorphe de taille proche quelconque et avec une direction pré-fixée suffisamment proche. Nous appliquons ces résultats aux pseudodistances de Kobayashi et Hanh. Nous montrons qu'elles coı̈ncident en dimensions supérieures à quatre. Le résultat est nouveau, même dans le cas complexe.
We simplify the proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close direction. We apply these results to the Kobayashi and Hanh pseudodistances. It is shown they coincide in dimensions higher than four. The result is new even in the complex case.
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@article{CRMATH_2004__338_4_295_0,
author = {Kruglikov, Boris},
title = {Deformation of big pseudoholomorphic disks and application to the {Hanh} pseudonorm},
journal = {Comptes Rendus. Math\'ematique},
pages = {295--299},
publisher = {Elsevier},
volume = {338},
number = {4},
year = {2004},
doi = {10.1016/j.crma.2003.12.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.12.010/}
}
TY - JOUR AU - Kruglikov, Boris TI - Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm JO - Comptes Rendus. Mathématique PY - 2004 SP - 295 EP - 299 VL - 338 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.12.010/ DO - 10.1016/j.crma.2003.12.010 LA - en ID - CRMATH_2004__338_4_295_0 ER -
%0 Journal Article %A Kruglikov, Boris %T Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm %J Comptes Rendus. Mathématique %D 2004 %P 295-299 %V 338 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.12.010/ %R 10.1016/j.crma.2003.12.010 %G en %F CRMATH_2004__338_4_295_0
Kruglikov, Boris. Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm. Comptes Rendus. Mathématique, Tome 338 (2004) no. 4, pp. 295-299. doi : 10.1016/j.crma.2003.12.010. http://www.numdam.org/articles/10.1016/j.crma.2003.12.010/
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