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1.
It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given. 相似文献
2.
It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is
determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for
a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the
source manifold into the target. An application to the biholomorphic equivalence problem is also given.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
3.
Baouendi M. S. Mir Nordine Rothschild Linda Preiss 《Journal of Geometric Analysis》2002,12(4):543-580
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂ
N
are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map
is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic
submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs
of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that
if two real-algebraic hypersurfaces in ℂ
N
are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general
context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds. 相似文献
4.
Jean-Charles Sunyé 《Journal of Geometric Analysis》2009,19(4):944-962
Let H:(M,p)→(M ′,p ′) be a formal mapping between two germs of real-analytic generic submanifolds in ? N with nonvanishing Jacobian. Assuming M to be minimal at p and M ′ holomorphically nondegenerate at p ′, we prove the convergence of the mapping H. As a consequence, we obtain a new convergence result for arbitrary formal maps between real-analytic hypersurfaces when the target does not contain any holomorphic curve. In the case when both M and M ′ are hypersurfaces, we also prove the convergence of the associated reflection function when M is assumed to be only minimal. This allows us to derive a new Artin type approximation theorem for formal maps of generic full rank. 相似文献
5.
Sergey Pinchuk Kaushal Verma 《Proceedings of the American Mathematical Society》2001,129(9):2623-2632
It is shown that if a continuous CR mapping between smooth real analytic hypersurfaces of finite type in extends as an analytic set, then it extends as a holomorphic mapping.
6.
In this article, we consider the question of when a holomorphic mapping on a domain in a complex Hilbert space into itself
has a holomorphic inverse. We give a strengthened version of a known result that involves a Fredholm condition on the mapping.
We show that holomorphic mappings on certain domains that are biholomorphic near the boundary are biholomorphic on the domain
itself.
相似文献
7.
Atsushi Hayashimoto 《复变函数与椭圆型方程》2020,65(3):423-439
ABSTRACTWe classify proper holomorphic mappings between generalized pseudoellipsoids of different dimensions. Those domains are parametrized by the exponents. The relations among them are also obtained. Main tool is the orthogonal decomposition of a CR bundle. Such a decomposition derives the ‘variable-splitting’ of the mapping. 相似文献
8.
Xu Cheng 《Geometriae Dedicata》2002,90(1):115-125
In this paper, we consider the coisotropic submanifolds in a Kähler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kähler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kähler manifolds. 相似文献
9.
Giuseppe Zampieri 《Journal of Mathematical Analysis and Applications》2003,283(1):150-158
Let be a CR mapping between real analytic generic submanifolds M, M1 of and , respectively. According to Webster's theory (Proc. Amer. Math. Soc. 86 (1982) 236-240) and its further developments, f has holomorphic extension to a full neighborhood of M in when the following requirements are fulfilled: f extends to a wedge W continuous up to M; f is of class Ck; (where denotes the complex tangent bundle); M1 is “k-nondegenerate.” We deal here with the case where is strictly smaller than but is still real analytic in suitable sense. We show that a suitably refined condition of k-nondegeneracy still entails holomorphic extension of f. 相似文献
10.
The E. Amar and G. Henkin theorem on the bounded extendability of bounded holomorphic functions from certain closed complex
submanifolds of strictly pseudoconvex domains to the whole domain is generalized to the case of finite type convex domains
and their intersections with affine linear hyperplanes. Suitable integral operators of Berndtsson–Andersson type are constructed
and estimated for this purpose.
Received: 7 July 2000 相似文献