Comptes Rendus
no. 4
Differential Geometry/Complex Analysis
Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm
[Déformation de grands disques pseudo-holomorphes et application à la pseudonorme de Hanh]

Présenté par : Mikhaël Gromov

Boris Kruglikov1
1 Mathematics-Statistics Department, University of Tromsø, 90-37, Tormosø, Norway
Comptes Rendus. Mathématique, Volume 338 (2004) no. 4, pp. 295-299.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.12.010
Boris Kruglikov 1

1 Mathematics-Statistics Department, University of Tromsø, 90-37, Tormosø, Norway 
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Boris Kruglikov. Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm. Comptes Rendus. Mathématique, Volume 338 (2004) no. 4, pp. 295-299. doi : 10.1016/j.crma.2003.12.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.010/

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