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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Complete localization of domains with noncompact automorphism groups

Author: Kang-Tae Kim
Journal: Trans. Amer. Math. Soc. 319 (1990), 139-153
MSC: Primary 32H20; Secondary 32A40, 32F15, 32M05
MathSciNet review: 986028
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Abstract: We prove a characterization of the domains in $ {{\mathbf{C}}^n}$ with an automorphism orbit accumulating at a boundary point at which the boundary is real analytic and convex up to a biholomorphic change of local coordinates. This result generalizes the well-known Wong-Rosay theorem on strongly pseudoconvex domains to the case of locally convex domains with real analytic boundaries.

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  • [1] J. D'Angelo, Real hypersurfaces, orders of contact, applications, Ann. of Math. 115 (1982), 615-637. MR 657241 (84a:32027)
  • [2] S. Frankel, Bounded convex domains with compact quotients are symmetric spaces in complex dimension two, Thesis, Stanford Univ., 1986.
  • [3] R. E. Greene and S. G. Krantz, Deformation of complex structures, estimates for the $ \overline \partial $ equation, and stability of the Bergman kernel, Adv. in Math. 43 (1982), 1-86. MR 644667 (84b:32026)
  • [4] -, Characterizations of certain weakly pseudoconvex domains with non-compact automorphism groups, Complex Analysis, Seminar, University Park, Pa., 1986, Lecture Notes in Math., vol. 1268, Springer-Verlag, 1987.
  • [5] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Marcel Dekker, New York, 1970. MR 0277770 (43:3503)
  • [6] S. Pinchuk, Holomorphic inequivalences of some classes of domains in $ {{\mathbf{C}}^n}$, Math. USSR Sb. 39 (1981), 61-86.
  • [7] J.-P. Rosay, Sur une caracterization de la boule parmi les domaines de $ {{\mathbf{C}}^n}$ par son groupe d'automorphismes, Ann. Inst. Fourier (Grenoble) 29 (1979), 91-97. MR 558590 (81a:32016)
  • [8] B. Wong, Characterization of the ball in $ {{\mathbf{C}}^n}$ by its automorphism group, Invent. Math. 41 (1977), 253-257. MR 0492401 (58:11521)

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