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Let F be an automorphism of which has an attracting fixed point. It is well known that the basin of attraction is biholomorphically equivalent to . We will show that the basin of attraction of a sequence of automorphisms f 1, f 2, . . . is also biholomorphic to if every f n is a small perturbation of the original map F.  相似文献   

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We show that any finitely connected domain can be properly embedded into . For some sequences can also be properly embedded into .  相似文献   

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We find explicitly all complex geodesics in a class of convex bounded Reinhardt domains ofC n, which are a generalization of complex ellipsoids. Entrata in Redazione il 19 maggio 1998.  相似文献   

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On leave from: Mathematisches Institut, Bunsenstrasse 3-5, D-37073, Göttingen, Germany  相似文献   

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We prove that if M is a connected real-analytic holomorphically nondegenerate hypersurface in Cn+1, then for any point pM there exists an integer k such that any two germs at p of local biholomorphic mappings that send M into itself and whose k-jets agree at p are identical.The above is a special case of a more general theorem stated for formal hypersurfaces that gives a finite jet determination result for the class of formal mappings whose Jacobian determinant does not vanish identically.  相似文献   

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In this paper, we study degenerate CR embeddings ff of a strictly pseudoconvex hypersurface M⊂Cn+1MCn+1 into a sphere SS in a higher dimensional complex space CN+1CN+1. The degeneracy of the mapping ff will be characterized in terms of the ranks of the CR second fundamental form and its covariant derivatives. In 2004, the author, together with X. Huang and D. Zaitsev, established a rigidity result for CR embeddings ff into spheres in low codimensions. A key step in the proof of this result was to show that degenerate mappings are necessarily contained in a complex plane section of the target sphere (partial rigidity). In the 2004 paper, it was shown that if the total rank dd of the second fundamental form and all of its covariant derivatives is <n<n (here, nn is the CR dimension of MM), then f(M)f(M) is contained in a complex plane of dimension n+d+1n+d+1. The converse of this statement is also true, as is easy to see. When the total rank dd exceeds nn, it is no longer true, in general, that f(M)f(M) is contained in a complex plane of dimension n+d+1n+d+1, as can be seen by examples. In this paper, we carry out a systematic study of degenerate CR mappings into spheres. We show that when the ranks of the second fundamental form and its covariant derivatives exceed the CR dimension nn, then partial rigidity may still persist, but there is a “defect” kk that arises from the ranks exceeding nn such that f(M)f(M) is only contained in a complex plane of dimension n+d+k+1n+d+k+1. Moreover, this defect occurs in general, as is illustrated by examples.  相似文献   

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We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as a product of proper mappings between the factor domains.  相似文献   

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Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism.  相似文献   

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We consider holomorphic mappings sending a given Levi-nondegenerate pseudoconcave hypersurface M in Cn+1 into a nondegenerate hyperquadric of the same signature in PCN+1 and show that if M is sufficiently close to a hyperquadric in a certain sense, then any two such mappings differ only by an automorphism of the hyperquadric.  相似文献   

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We describe all proper holomorphic mappings of the symmetrized polydisc and study its geometric properties. We also apply the obtained results to the study of the spectral unit ball in Received: 8 June 2004  相似文献   

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We study the problem of existence of stationary disks for domains in almost complex manifolds. As a consequence of our results, we prove that any almost complex domain which is a small deformation of a strictly linearly convex domain DCn with standard complex structure admits a singular foliation by stationary disks passing through any given internal point. Similar results are given for foliations by stationary disks through a given boundary point.  相似文献   

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Since a paper by Rosay and Rudin (Trans. Am. Math. Soc. 310, 47–86, 1988) there has been an open question whether all Fatou–Bieberbach domains are Runge. We give an example of a Fatou–Bieberbach domain Ω in which is not Runge. The domain Ω provides (yet) a negative answer to a problem of Bremermann. Supported by Schweizerische Nationalfonds grant 200021-116165/1.  相似文献   

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