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A. V. Loboda 《Mathematical Notes》1995,57(6):606-614
This work was partially supported by the Russian Foundation for Fundamental Research, Grant No. 93-011-255. 相似文献
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Tommaso de Fernex 《Inventiones Mathematicae》2013,192(3):533-566
We prove that for N≥4, all smooth hypersurfaces of degree N in ? N are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals. 相似文献
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Sung-Yeon Kim 《Journal of Mathematical Analysis and Applications》2010,366(2):418-434
In this paper we show that a C∞ real hypersurface in Cn+1 of finite D'Angelo type admitting a weakly contracting local CR automorphism is CR equivalent to a weighted homogeneous hypersurface. As an application, we show that a bounded pseudoconvex domain in Cn+1 with C∞ boundary of finite D'Angelo type with a hyperbolic orbit accumulation point is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial. 相似文献
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Jih-Hsin Cheng 《Proceedings of the American Mathematical Society》2000,128(6):1825-1832
We establish Bochner-type formulas for operators related to automorphisms and spherical structures. From such formulas, we draw conclusions about rigidity by making assumptions on the Tanaka-Webster curvature and torsion.
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Oblatum 8-VI-1995 & 18-X-1995 相似文献
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Luca Baracco 《Journal of Mathematical Analysis and Applications》2007,331(1):220-229
We prove extension of CR functions from a hypersurface M of CN in presence of the so-called sector property. If M has finite type in the Bloom-Graham sense, then our result is already contained in [C. Rea, Prolongement holomorphe des fonctions CR, conditions suffisantes, C. R. Acad. Sci. Paris 297 (1983) 163-166] by Rea. We think however, that the argument of our proof carries an expressive geometric meaning and deserves interest on its own right. Also, our method applies in some case to hypersurfaces of infinite type; note that for these, the classical methods fail. CR extension is treated by many authors mainly in two frames: extension in directions of iterated of commutators of CR vector fields (cf., for instance, [A. Boggess, J. Pitts, CR extension near a point of higher type, Duke Math. J. 52 (1) (1985) 67-102; A. Boggess, J.C. Polking, Holomorphic extension of CR functions, Duke Math. J. 49 (1982) 757-784. [4]; M.S. Baouendi, L. Rothschild, Normal forms for generic manifolds and holomorphic extension of CR functions, J. Differential Geom. 25 (1987) 431-467. [1]]); extension through minimality towards unprecised directions [A.E. Tumanov, Extension of CR-functions into a wedge, Mat. Sb. 181 (7) (1990) 951-964. [6]; A.E. Tumanov, Analytic discs and the extendibility of CR functions, in: Integral Geometry, Radon Transforms and Complex Analysis, Venice, 1996, in: Lecture Notes in Math., vol. 1684, Springer, Berlin, 1998, pp. 123-141]. 相似文献
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Zaifei Ye 《Journal of Geometric Analysis》1992,2(4):381-387
We show that if a CR homeomorphism can be holomorphically extended to a neighborhood of a nonminimal point (in Tumanov's sense), then the extended map is proper, and, near a minimal point, the holomorphic extension is biholomorphic in a neighborhood of the point. 相似文献
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Research was supported by Max-Planck-Institut Bonn 相似文献
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Jiří Lebl 《Journal of Geometric Analysis》2007,17(2):321-341
A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension
is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being
contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely
resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic
submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic
one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces. 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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A. S. Labovskii 《Mathematical Notes》1997,61(3):287-294
In this paper we study the dependence of the local geometry of real-analytic hypersuffaces in ℂ
n
on the dimension of the group of biholomorphic automorphisms of this surface. We also classify the hypersurfaces in terms
of this group. We present some examples showing that the classes of the given construction are not empty. We find a new formulation
of the Freeman theorem on the so-called straightening of a real-analytic CR-submanifold in ℂ
n
with degenerate Levi form of constant rank.
Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 349–358, March, 1997.
Translated by E. G. Anisova 相似文献
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Peter Ebenfelt 《Mathematische Annalen》2002,322(3):583-602
Let be a connected real-analytic hypersurface containing a connected complex hypersurface , and let be a smooth CR mapping sending M into another real-analytic hypersurface . In this paper, we prove that if f does not collapse E to a point and does not collapse M into the image of E, and if the Levi form of M vanishes to first order along E, then f is real-analytic in a neighborhood of E. In general, the corresponding statement is false if the Levi form of M vanishes to second order or higher, in view of an example due to the author. We also show analogous results in higher dimensions
provided that the target M' satisfies a certain nondegeneracy condition. The main ingredient in the proof, which seems to be of independent interest,
is the prolongation of the system defining a CR mapping sending M into M' to a Pfaffian system on M with singularities along E. The nature of the singularity is described by the order of vanishing of the Levi form along E.
Received: 12 February 2001 / Published online: 18 January 2002 相似文献
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