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2.
本文在复空间C_t×C_x上讨论了一类非线性全特征型具正则奇性偏微分方程组的全纯解,在一定的条件下,证明了在复空C_t×C_x的原点附近的某个邻域内存在唯一的全纯解,并把结论推广到了高阶的情况.本文的结果实际上是经典的Cauchy-Kowalewski定理在非线性奇异方程组上的推广。 相似文献
3.
严荣沐 《数学物理学报(A辑)》2006,(Z1)
In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain). 相似文献
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RANDOMITERATIONOFHOLOMORPHICSELF-MAPSOVERBOUNDEDDOMAINSINC~N¥ZHANGWENJUN;RENFUYAO(DeparatmentofMathematics,HenalUniversitytKa?.. 相似文献
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研究了具有一定性质的全纯函数.设F是平面上区域D内的全纯函数族.如果对于任意的f∈F 都有 其中C为常数且f(0)≠0,则F正规. 相似文献
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本文主要证明一类广义Hartogs三角形之间的逆紧全纯映射在相差全纯自同构的意义下是唯一的。 相似文献
7.
设D是扩充复平面R-2中的单连通Jordan真子域,D*=R-2\D-是D的外部.本文肯定并证明 了K.Hag在1999年提出的如下两个悬而未决的问题:(1)D是Cigar域当且仅当D是OLC域; (2)D是Turning域当且仅当D*是Cigar域. 相似文献
8.
Ngaiming Mok 《数学物理学报(B辑英文版)》2009,29(4):881-902
In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometrics up to normalizing constants with respect to the Bergman metric, showing in particular that the graph 170 of any germ of holomorphic isometry of the Poincar6 disk A into an irreducible bounded symmetric domain Ω belong to C^N in its Harish-Chandra realization must extend to an affinealgebraic subvariety V belong to C × C^N = C^N+1, and that the irreducible component of V ∩ (△ × Ω) containing V0 is the graph of a proper holomorphic isometric embedding F : A→ Ω. In this article we study holomorphie isometric embeddings which are asymptotically geodesic at a general boundary point b ∈ δ△. Starting with the structural equation for holomorphic isometrics arising from the Gauss equation, we obtain by covariant differentiation an identity relating certain holomorphic bisectional curvatures to the boundary behavior of the second fundamental form σ of the holomorphie isometric embedding. Using the nonpositivity of holomorphic bisectional curvatures on a bounded symmetric domain, we prove that ‖σ‖ must vanish at a general boundary point either to the order 1 or to the order 1/2, called a holomorphie isometry of the first resp. second kind. We deal with special cases of non-standard holomorphic isometric embeddings of such maps, showing that they must be asymptotically totally geodesic at a general boundary point and in fact of the first kind whenever the target domain is a Cartesian product of complex unit balls. We also study the boundary behavior of an example of holomorphic isometric embedding from the Poincare disk into a Siegel upper half-plane by an explicit determination of the boundary behavior of holomorphic sectional curvatures in the directions tangent to the embedded Poincare disk, showing that the map is indeed asymptotically totally geodesic at a general boundary point and of the first kind. For the metric computation we make use of formulas for symplectic geometry on Siegel upper half-planes. 相似文献
9.
ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES 总被引:1,自引:0,他引:1
In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct x Cxn. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct x Cxn. 相似文献