On the automorphism group of strongly pseudoconvex domains in almost complex manifolds

Jisoo Byun[1]; Hervé Gaussier[2]; Kang-Hyurk Lee[3]

  • [1] Department of Mathematics POSTECH Pohang, 790-784 (Korea)
  • [2] CMI 39 rue Joliot-Curie 13453 Marseille Cedex 13 (France)
  • [3] School of Mathematics KIAS, Hoegiro 87 Dongdaemun-gu Seoul, 130-722 (Korea)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 1, page 291-310
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Byun, Jisoo, Gaussier, Hervé, and Lee, Kang-Hyurk. "On the automorphism group of strongly pseudoconvex domains in almost complex manifolds." Annales de l’institut Fourier 59.1 (2009): 291-310. <http://eudml.org/doc/10393>.

@article{Byun2009,
abstract = {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.},
affiliation = {Department of Mathematics POSTECH Pohang, 790-784 (Korea); CMI 39 rue Joliot-Curie 13453 Marseille Cedex 13 (France); School of Mathematics KIAS, Hoegiro 87 Dongdaemun-gu Seoul, 130-722 (Korea)},
author = {Byun, Jisoo, Gaussier, Hervé, Lee, Kang-Hyurk},
journal = {Annales de l’institut Fourier},
keywords = {Automorphism groups; strongly pseudoconvex domains; almost complex manifolds; non-integrable deformations; automorphism groups},
language = {eng},
number = {1},
pages = {291-310},
publisher = {Association des Annales de l’institut Fourier},
title = {On the automorphism group of strongly pseudoconvex domains in almost complex manifolds},
url = {http://eudml.org/doc/10393},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Byun, Jisoo
AU - Gaussier, Hervé
AU - Lee, Kang-Hyurk
TI - On the automorphism group of strongly pseudoconvex domains in almost complex manifolds
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 1
SP - 291
EP - 310
AB - 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.
LA - eng
KW - Automorphism groups; strongly pseudoconvex domains; almost complex manifolds; non-integrable deformations; automorphism groups
UR - http://eudml.org/doc/10393
ER -

References

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