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Tytuł artykułu

The automorphism groups of domains and the Greene-Krantz conjecture

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the subject of the automorphism groups of domains in complex space. In particular, we describe and discuss the noted Greene–Krantz conjecture.
Rocznik
Strony
807--817
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri, USA 63130
Bibliografia
  • [1] J. Bland, T. Duchamp, M. Kalka, A characterization of CPn by its automorphism group, [in]: S.G. Krantz (ed.), Complex Analysis, Lecture Notes in Mathematics, vol. 1268, Springer, Berlin, Heidelberg, 1987, 60–65.
  • [2] E. Bedford, S. Pinchuk, Domains in C2 with noncompact groups of holomorphic automorphisms, Mat. Sb. (N.S.) 135 (1988), 147–157 [in Russian].
  • [3] E. Bedford, S. Pinchuk, Domains in Cn+1 with noncompact automorphism group, J. Geom. Anal. 1 (1991), 165–191.
  • [4] E. Bedford, S. Pinchuk, Convex domains with noncompact groups of automorphisms, Mat. Sb. 185 (1994), 3–26 [in Russian], translation in Russian Acad. Sci. Sb. Math. 82 (1995), 1–20.
  • [5] E. Bedford, S. Pinchuk, Domains in C2 with noncompact automorphism groups, Indiana Univ. Math. J. 47 (1998), 199–222.
  • [6] D. Catlin, Subelliptic estimates for the ∂-Neumann problem, Ann. Math. 126 (1987), 131–192.
  • [7] J.P. D’Angelo, Several Complex Variables and the Geometry of Real Hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993.
  • [8] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65.
  • [9] S. Frankel, Complex geometry of convex domains that cover varieties, Acta Math. 163 (1989), 109–149.
  • [10] I. Graham, Boundary behavior of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains in Cn with smooth boundary, Trans. Amer. Math. Soc. 207 (1975), 219–240.
  • [11] R.E. Greene, S.G. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261 (1982), 425–446.
  • [12] R.E. Greene, S.G. Krantz, Characterization of complex manifolds by the isotropy subgroups of their automorphism groups, Indiana Univ. Math. J. 34 (1985), 865–879.
  • [13] R.E. Greene, S.G. Krantz, Invariants of Bergman geometry and the automorphism groups of domains in Cn, [in:] Geometrical and algebraical aspects in several complex variables (Cetraro, 1989), 107–136, Sem. Conf., 8, EditEl, Rende, 1991.
  • [14] R.E. Greene, K.T. Kim, S.G. Krantz, The Geometry of Complex Domains, Progress in Mathematics, 291, Birkhäuser Boston, Ltd., Boston, MA, 2011.
  • [15] R.E. Greene, K.T. Kim, S.G. Krantz, A. Seo, Semicontinuity of automorphism groups of strongly pseudoconvex domains: the low differentiability case, Pacific J. Math. 262 (2013), 365–395.
  • [16] A.V. Isaev, S.G. Krantz, Domains with non-compact automorphism group: a survey, Adv. Math. 146 (1999), 1–38.
  • [17] K.-T. Kim, Complete localization of domains with noncompact automorphism group, Trans. Amer. Math. Soc. 319 (1990), 139–153.
  • [18] K.-T. Kim, Domains in Cn with a piecewise Levi flat boundary which possess a noncompact automorphism group, Math. Ann. 292 (1992), 575–586.
  • [19] K.-T. Kim, S.G. Krantz, Normal families of holomorphic functions and mappings on a Banach space, Expo. Math. 21 (2003), 193–218.
  • [20] J.J. Kohn, Boundary behavior of ∂ on weakly pseudoconvex manifolds of dimension two, J. Differential Geom. 6 (1972), 523–542.
  • [21] S.G. Krantz, Function Theory of Several Complex Variables, 2nd ed., AMS Chelsea Publishing, Providence, RI, 2001.
  • [22] S.G. Krantz, The Greene–Krantz conjecture in dimension two, Rocky Mountain J. Math. 46 (2016), 1575–1586.
  • [23] B. Liu, Analysis of orbit accumulation points and the Greene–Krantz conjecture, J. Geom. Anal. 27 (2017), 726–745.
  • [24] S. Pinchuk, The scaling method and holomorphic mappings, [in:] Several Complex Variables and Complex Geometry, Part 1 (Santa Cruz, CA, 1989), Proc. Sympos. Pure Math., 52, Part 1, Amer. Math. Soc., Providence, RI, 1991.
  • [25] J.-P. Rosay, Sur une caractérisation de la boule parmi les domains de Cn par son groupe d’automorphismes, Ann. Inst. Four. Grenoble 29 (1979), 91–97.
  • [26] G. Tsai, A characterization of bounded convex domains in Cn with non-compact automorphism group, preprint.
  • [27] N. Van Thu, Problems about the Greene–Krantz conjecture, preprint.
  • [28] B. Wong, Characterizations of the ball in Cn by its automorphism group, Invent. Math. 41 (1977), 253–257.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d161889c-f469-4a47-be42-bcbc303aee2a
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