Abstract
In this paper, we introduce the Wong-Rosay theorem, R. Schoen’s theorem and its generalization in almost complex geometry.
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References
Alekseevski\(\breve{I}\), D.V.: Groups of conformal transformations of Riemannian spaces. Mat. Sb. (N.S.) 89(131), 280–296, 356 (1972)
Burns Jr, D., Shnider, S., Wells Jr, R.O.: Deformations of strictly pseudoconvex domains. Invent. Math. 46, 237–253 (1978)
Byun, J., Gaussier, H., Lee, K.-H.: On the automorphism group of strongly pseudoconvex domains in almost complex manifolds. Ann. Inst. Fourier (Grenoble) 59, 291–310 (2009)
Efimov, A.M.: A generalization of the Wong-Rosay theorem for the unbounded case. Mat. Sb. 186, 41–50 (1995)
Falbel, E., Veloso, J.M.: A bilinear form associated to contact sub-conformal manifolds. Differ. Geom. Appl. 25, 35–43 (2007)
Falbel, E., Veloso, J.M., Verderesi, J.A.: Constant curvature models in sub-Riemannian geometry. Mat. Contemp. 4, 119–125 (1993). VIII School on Differential Geometry (Portuguese) (Campinas, 1992)
Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math. 26, 1–65 (1974)
Ferrand, J.: The action of conformal transformations on a Riemannian manifold. Math. Ann. 304, 277–291 (1996)
Gaussier, H., Kim, K.-T., Krantz, S.G.: A note on the Wong-Rosay theorem in complex manifolds. Complex Var. Theory Appl. 47, 761–768 (2002)
Gaussier, H., Sukhov, A.: Wong-Rosay theorem in almost complex manifolds, preprint, arXiv:math/0307335
Gaussier, H., Sukhov, A.: On the geometry of model almost complex manifolds with boundary. Math. Z. 254, 567–589 (2006)
Greene, R.E., Krantz, S.G.: Deformation of complex structures, estimates for the \(\bar{\partial }\) equation, and stability of the Bergman kernel. Adv. Math. 43, 1–86 (1982)
Jerison, D., Lee, J.M.: The Yamabe problem on CR manifolds. J. Differ. Geom. 25, 167–197 (1987)
Joo, J.-C., Lee, K.-H.: Subconformal Yamabe equation and automorphism groups of almost CR manifolds, J. Geom. Anal., to appear
Lee, K.-H.: Domains in almost complex manifolds with an automorphism orbit accumulating at a strongly pseudoconvex boundary point. Mich. Math. J. 54, 179–205 (2006)
Lee, K.-H.: Strongly pseudoconvex homogeneous domains in almost complex manifolds, J. Reine Angew. Math. 623, 123–160 (2008)
Rosay, J.-P.: Sur une caractérisation de la boule parmi les domaines de \({\bf C}^{n}\,\) par son groupe d’automorphismes. Ann. Inst. Fourier (Grenoble), 29, ix, 91–97 (1979)
Schoen, R.: On the conformal and CR automorphism groups. Geom. Funct. Anal. 5, 464–481 (1995)
Webster, S.M.: Pseudo-Hermitian structures on a real hypersurface. J. Differ. Geom. 13, 25–41 (1978)
Wong, B.: Characterization of the unit ball in \({ C}^{n}\) by its automorphism group. Invent. Math. 41, 253–257 (1977)
Acknowledgments
The research of the author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF 2012R1A1A1004849).
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Lee, KH. (2015). Characterizations of Strongly Pseudoconvex Models in Almost Complex and CR Geometries. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_16
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DOI: https://doi.org/10.1007/978-4-431-55744-9_16
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