On the automorphism group of strongly pseudoconvex domains in almost complex manifolds
Annales de l'Institut Fourier, Volume 59 (2009) no. 1, p. 291-310

In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.

We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost complex manifolds under deformation of the structure.

Contrairement au cas intégrable, il existe une infinité de variétés presque complexes homogènes, non intégrables, strictement pseudoconvexes en tout point de leur bord. De telles variétés sont équivalentes au demi-espace de Siegel muni d’une structure presque complexe linéaire.

Nous démontrons qu’il n’existe pas de représentation relativement compacte, strictement pseudoconvexe, de ces variétés. Enfin, nous étudions la semi-continuité du groupe des automorphismes de certaines variétés presque complexes hyperboliques, strictement pseudoconvexes, par déformation de la structure.

DOI : https://doi.org/10.5802/aif.2431
Classification:  32G05,  32H02,  32T15,  53C15
Keywords: Automorphism groups, strongly pseudoconvex domains, almost complex manifolds
@article{AIF_2009__59_1_291_0,
     author = {Byun, Jisoo and Gaussier, Herv\'e and Lee, Kang-Hyurk},
     title = {On the automorphism group of strongly pseudoconvex domains in almost complex manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {1},
     year = {2009},
     pages = {291-310},
     doi = {10.5802/aif.2431},
     mrnumber = {2514866},
     zbl = {1168.32021},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_1_291_0}
}
Byun, Jisoo; Gaussier, Hervé; Lee, Kang-Hyurk. On the automorphism group of strongly pseudoconvex domains in almost complex manifolds. Annales de l'Institut Fourier, Volume 59 (2009) no. 1, pp. 291-310. doi : 10.5802/aif.2431. http://www.numdam.org/item/AIF_2009__59_1_291_0/

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