Abstract
In this paper, we give an explicit description for the automorphism groups of finite multitype models in \(\mathbb C^n\).
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Ahn, T., Gaussier, H., Kim, K.-T.: Positivity and completeness of invariant metrics. J. Geom. Anal. 26(2), 1173–1185 (2016)
Bedford, E., Pinchuk, S.: Convex domains with noncompact groups of automorphisms. Math. Sb. 185(5), 3–26 (1994). translation in Russian Acad. Sci. Sb. Math. 82 (1995), no. 1, 1–20
Bell, S., Ligocka, E.: A simplification and extension of Fefferman’s theorem on biholomorphic mappings. Invent. Math. 57(3), 283–289 (1980)
Berteloot, F.: Characterization of models in \(\mathbb{C}^2\) by their automorphism groups. Int. J. Math. 5(5), 619–634 (1994)
Catlin, D.: Global regularity of the \(\bar{\partial }\)-Neumann problem. Proc. Sympos. Pure Math. 41, 39–49 (1984)
Catlin, D.: Boundary invariants of pseudoconvex domains. Ann. Math. 120(3), 529–586 (1984)
D’Angelo, J.P.: A remark on finite type conditions, to appear. J. Geom. Anal. 25(3), 1701–1719 (2017)
Fu, S., Isaev, A., Krantz, S.: Reinhardt domains with non-compact automorphism groups. Math. Res. Lett. 3(1), 109–122 (1996)
Fu, S., Isaev, A., Krantz, S.: Examples of domains with non-compact automorphism groups. Math. Res. Lett. 3(5), 609–617 (1996)
Gaussier, H.: Characterization of convex domains with noncompact automorphism group. Michigan Math. J. 44(2), 375–388 (1997)
Gaussier, H.: Tautness and complete hyperbolicity of domains in \(\mathbb{C}^n\). Proc. Am. Math. Soc. 127(1), 105–116 (1999)
Herbort, G.: On the Bergman distance on model domains in \(\mathbb{C}^n\). Ann. Pol. Math. 116(1), 1–36 (2016)
Isaev, A., Krantz, S.G.: Domains with non-compact automorphism group: a survey. Adv. Math. 146, 1–38 (1999)
Kim, K.-T., Ninh, V.T.: On the tangential holomorphic vector fields vanishing at an infinite type point. Trans. Am. Math. Soc. 367(2), 867–885 (2015)
Kohn, J.J., Nirenberg, L.: A pseudo-convex domain not admitting a holomorphic support function. Math. Ann. 201, 265–268 (1973)
Kolar, M.: The Catlin multitype and biholomorphic equivalence of models. Int. Math. Res. Not. IMRN 18, 3530–3548 (2010)
Kolar, M., Meylan, F., Zaitsev, D.: Chern-Moser operators and polynomial models in CR geometry. Adv. Math. 263, 321–356 (2014)
Kolar, M., Meylan, F.: Higher order symmetries of real hypersurfaces in \(\mathbb{C}^3\). Proc. Am. Math. Soc. 144(11), 4807–4818 (2016)
Ninh, V.T., Mai, A.D.: On the automorphism groups of models in \(\mathbb{C}^2\). Acta Math. Vietnam. 41(3), 457–470 (2016)
Pinchuk, S., Shafikov, R.: Critical sets of proper holomorphic mappings. Proc. Am. Math. Soc. 143, 4335–4345 (2015)
Rong, F., Zhang, B.: On \(h\)-extendible domains and associated models. C. R. Math. Acad. Sci. Paris 354(9), 901–906 (2016)
Rosay, J.P.: Sur une caracterisation de la boule parmi les domaines de \(\mathbb{C}^n\) par son groupe d’automorphismes. Ann. Inst. Fourier 29(4), 91–97 (1979)
Sukhov, A.B.: On the boundary regularity of holomorphic mappings, (Russian) Mat. Sb. 185 (1994), no. 12, 131–142; translation in Russian Acad. Sci. Sb. Math. 83 (1995), no. 2, 541–551
Wong, B.: Characterization of the unit ball in \(\mathbb{C}^n\) by its automorphism group. Invent. Math. 41(3), 253–257 (1977)
Yu, J.: Multitypes of convex domains. Indiana Univ. Math. J. 41(3), 837–849 (1992)
Yu, J.: Peak functions on weakly pseudoconvex domains. Indiana Univ. Math. J. 43(4), 1271–1295 (1994)
Acknowledgements
The authors thank the referee for careful reading and valuable comments. Part of this work was done while the first and last authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). They would like to thank the VIASM for financial support and hospitality. The first and second authors were supported by NAFOSTED under Grant Number 101.02-2017.311 and the last author was supported by the National Research Foundation of Korea with Grant NRF-2015R1A2A2A11001367.
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Ninh, V.T., Nguyen, T.L.H., Tran, Q.H. et al. On the Automorphism Groups of Finite Multitype Models in \(\mathbb C^n\). J Geom Anal 29, 428–450 (2019). https://doi.org/10.1007/s12220-018-9999-0
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DOI: https://doi.org/10.1007/s12220-018-9999-0