Estimates of the Kobayashi-Royden metric in almost complex manifolds
Bulletin de la Société Mathématique de France, Volume 133 (2005) no. 2, pp. 259-273.

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M,J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M,J).

Nous établissons une estimée inférieure pour la métrique de Kobayashi-Royden sur une variété presque complexe (M,J) admettant une fonction bornée strictement pluri-sous-harmonique. Nous appliquons ce résultat à l’étude du comportement de la métrique au bord d’un domaine strictement pseudoconvexe dans M et donnons une condition suffisante d’hyperbolicité complète d’un domaine dans (M,J).

DOI: 10.24033/bsmf.2486
Classification: 32V40,  32V15,  32H40,  32T15,  53C15
Keywords: almost complex manifolds, Kobayashi-Royden metric, J-holomorphic discs
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     author = {Gaussier, Herv\'e and Sukhov, Alexandre},
     title = {Estimates of the {Kobayashi-Royden} metric in almost complex manifolds},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {259--273},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {133},
     number = {2},
     year = {2005},
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Gaussier, Hervé; Sukhov, Alexandre. Estimates of the Kobayashi-Royden metric in almost complex manifolds. Bulletin de la Société Mathématique de France, Volume 133 (2005) no. 2, pp. 259-273. doi : 10.24033/bsmf.2486. http://archive.numdam.org/articles/10.24033/bsmf.2486/

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