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991.
Let G i be a closed Lie subgroup of U(n), Ω i be a bounded G i -invariant domain in C n which contains 0, and \(O{\left( {{\mathbb{C}^n}} \right)^{{G_i}}} = \mathbb{C}\), for i = 1; 2. If f: Ω1 → Ω2 is a biholomorphism, and f(0) = 0, then f is a polynomial mapping (see Ning et al. (2017)). In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan’s theorem. 相似文献
992.
The main purpose of this paper is to generalize the celebrated L~2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact. 相似文献
993.
Yum-Tong Siu 《中国科学 数学(英文版)》2017,60(6):1101-1128
The purpose of this paper is threefold. (i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D’Angelo concerning the ineffectiveness of the latter. (ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations. (iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations. 相似文献
994.
Let G be a connected real reductive group with maximal compact subgroup K of the same rank as G. Dirac cohomology of an A_q(λ) module can be identified with a geometric object—the k-dominant part of a face of the convex hull of the Weyl group orbit of the parameter λ + ρ. We show how Dirac cohomology can be used as a parameter to classify the A_q(λ) modules. 相似文献
995.
In this paper, we derive W~(1,∞) and piecewise C~(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces. 相似文献
996.
In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II. 相似文献
997.
Let u =(uh, u3) be a smooth solution of the 3-D Navier-Stokes equations in R3× [0, T). It was proved that if u3 ∈ L∞(0, T;˙B-1+3/p p,q(R3)) for 3 p, q ∞ and uh∈ L∞(0, T; BMO-1(R3)) with uh(T) ∈ VMO-1(R3), then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al.(2016), which requires u ∈ L∞(0, T;˙B-1+3/pp,q(R3)). Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest. 相似文献
998.
Let X_1 and X_2 be two compact connected strongly pseudoconvex embeddable Cauchy-Riemann(CR) manifolds of dimensions 2m-1 and 2n-1 in C~(m+1)and C~(n+1), respectively. We introduce the ThomSebastiani sum X = X_1 ⊕X_2which is a new compact connected strongly pseudoconvex embeddable CR manifold of dimension 2m+2n+1 in C~(m+n+2). Thus the set of all codimension 3 strongly pseudoconvex compact connected CR manifolds in Cn+1for all n 2 forms a semigroup. X is said to be an irreducible element in this semigroup if X cannot be written in the form X_1 ⊕ X_2. It is a natural question to determine when X is an irreducible CR manifold. We use Kohn-Rossi cohomology groups to give a necessary condition of the above question. Explicitly,we show that if X = X_1 ⊕ X_2, then the Kohn-Rossi cohomology of the X is the product of those Kohn-Rossi cohomology coming from X_1 and X_2 provided that X_2 admits a transversal holomorphic S~1-action. 相似文献
999.
WeiPing Zhang 《中国科学 数学(英文版)》2017,60(9):1615-1632
We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin? manifolds. The analytic index is the reduced η invariant of (twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer (1971) to non-orientable manifolds. 相似文献
1000.
ChenYan Wu 《中国科学 数学(英文版)》2017,60(2):201-222
Letπbe a genuine cuspidal representation of the metaplectic group of rank n.We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n+1.We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central value of the Langlands L-function ofπtwisted by a character.The bulk of this paper focuses on proving a case of regularised Siegel-Weil formula,on which the Rallis inner product formula is based and whose proof is missing in the literature. 相似文献