共查询到20条相似文献,搜索用时 875 毫秒
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本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域ΩBm(μ)不是球,则它上面存在一函数X使得它在ΩBm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域ΩBm(μ)不是球,ΩBm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变. 相似文献
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设U≥0表示一个固定单李代数的半量子群,给出了U≥0的性质和表示. 证明了Hopf代数U≥0不是拟余交换的,因此左U≥0模范畴不是辫子monoidal范畴. 在权模范畴W中,给出了所有单对象和投射对象. 最后描述了所有单的Yetter-Drinfel'd U≥0权模. 相似文献
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本文研究了环Fpm+uFpm+u2Fpm上长度为ps的循环码分类.通过建立环Fpm+uFpm+u2Fpm到环Fpm+uFpm的同态,给出了环Fpm+uFpm+u2Fpm上长度为ps的循环码的新分类方法.应用这种方法,得到了环Fpm+uFpm+u2Fpm长度为ps的循环码的码词数. 相似文献
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本文研究了有限域上置换多项式的构造问题.利用分段方法构造了Fq2上形如(xq-x+c)(k(q2-1))/(d)+1+xq+x的置换多项式,其中1≤k < d且d是q-1的任意因子,推广了已有文献中的某些结果. 相似文献
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本文引入了近切触流形(M,ø,ξ,η,g)中φ*-解析向量场的概念,并研究了其性质.利用近切触流形的性质,证明了切触度量流形中的φ*-解析向量场v是Killing向量场且φv不是φ*-解析的.特别地,如果近切触流形M是正规的,得到v与ξ平行且模长为常数.另外,证明了3维的切触度量流形不存在非零的φ*-解析向量场. 相似文献
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Shimpei Kobayashi 《Annals of Global Analysis and Geometry》2009,36(4):375-380
We give a simple criterion for equivariant harmonic maps into complex projective spaces CP
n
. As an application of the criterion, we give examples of equivariant harmonic cylinders. We also give examples of non-equivariant
harmonic cylinders as perturbations of equivariant harmonic cylinders. 相似文献
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The Debye source representation for solutions to the time‐harmonic Maxwell equations is extended to bounded domains with finitely many smooth boundary components. A strong uniqueness result is proved for this representation. Natural complex structures are identified on the vector spaces of time‐harmonic Maxwell fields. It is shown that these complex structures are uniformized by the Debye source representation, that is, represented by a fixed linear map on a fixed vector space, independent of the frequency. This complex structure relates time‐harmonic Maxwell fields to constant‐k Beltrami fields, i.e., solutions of the equation A family of self‐adjoint boundary conditions are defined for the Beltrami operator. This leads to a proof of the existence of zero‐flux, constant‐k, force‐free Beltrami fields for any bounded region in ?3, as well as a constructive method to find them. The family of self‐adjoint boundary value problems defines a new spectral invariant for bounded domains in ?3.© 2015 Wiley Periodicals, Inc. 相似文献
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Peter Lindqvist 《Israel Journal of Mathematics》1988,63(3):257-269
In the complex plane thep-harmonic equation div(|∇u|
p−2∇u) = 0, 1 <p < ∞, exhibits some features reminiscent of Function Theory. Our results about curvature in this structure complement known
facts about minimal surfaces and harmonic functions. Quasiregular mappings are used. 相似文献
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Peng Zhu 《Annals of Global Analysis and Geometry》2011,40(4):427-434
We prove that L
2 harmonic two-forms are parallel if a complete manifold (M, g) has the non-negative isotropic curvature. Furthermore, if (M, g) has positive isotropic curvature at some point, then there is no non-trivial L
2 harmonic two-form. We obtain that an almost K?hler manifold of non-negative isotropic curvature is K?hler and a symplectic
manifold can not admit any almost K?hler structure of positive isotropic curvature. 相似文献
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Three- dimensional analogs of rational uniform approximation in
\mathbbC \mathbb{C} are considered. These analogs are related to approximation properties of harmonic (i. e., curl-free and solenoidal) vector
fields. The usual uniform approximation by fields harmonic near a given compact set K ⊂
\mathbbR3 \mathbb{R}^3 is compared with the uniform approximation by smooth fields whose curls and divergences tends to zero uniformly on K. A similar two-dimensional modification of the uniform approximation by functions f that are complex analytic near a given compact set K ⊂
\mathbbC \mathbb{C} (when f is assumed to be in C
1 with [`(?)] f\bar \partial {\kern 1pt}f small on K) results in a problem equivalent to the original one. In the three-dimensional settings, the two problems (of harmonic and
of almost harmonic approximation) are different. The first problem is nonlocal whereas the second one is local (i. e., an
analog of the Bishop theorem on the locality of R(K) is still valid for almost harmonic approximation). Almost curl-free approximation is also considered. Bibliography: 7 titles. 相似文献
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Let , where B is the open unit ball in (), and let denote the collection of functions h in which are harmonic on B and satisfy on . A function h
* in is called a best harmonic one-sided L
1-approximant to f if for all h in . This paper characterizes such approximants and discusses questions of existence and uniqueness. Corresponding results for
approximation on the cylinder are also established, but the proofs in this case are more difficult and rely on recent work concerning tangential harmonic
approximation. The characterizations are quite different in nature from those recently obtained for harmonic L
1-approximation without a one-sidedness condition.
Received: 25 September 1997 相似文献
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There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S
1-valued function defined on the boundary of a bounded regular domain of R
n
. When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence,
a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic
map away from a codimension-2 minimal current minimizing the area within the homology class induced from the S
1-valued boundary data. The union of this harmonic map and the minimal current is the natural generalization of the harmonic
extension.
Received December 3, 1998 / final version received May 10, 1999 相似文献
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It is proved by purely algebraic method that weakly conformai, conformai andA
z
3
= 0 are mutually equivalent if ϕ :Ω→ℂP
n
is a non-isotropic harmonic map and the harmonic maps with isotropy order ≥3 are uniquely determined by a system of ordinary
differential equations. A method is given, by which the isotropy orders of non-isotropic harmonic maps can be computed. 相似文献
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Yu Ding 《Israel Journal of Mathematics》2002,129(1):241-251
In this paper we prove that when the Ricci curvature of a Riemannian manifoldM
n
is almost nonnegative, and a ballB
L
(p)⊂M
n
is close in Gromov-Hausdorff distance to a Euclidean ball, then the gradient of the harmonic functionb defined in [ChCo1] does not vanish. In particular, these functions can serve as harmonic coordinates on balls sufficiently
close to an Euclidean ball. The proof, is based on a monotonicity theorem that generalizes monotonicity of the frequency for
harmonic functions onR
n
. 相似文献
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In this paper, by using the technique of integral transformation, we obtain the Plemelj formulas with the Cauchy principal value and the Hadamard principal value of mixed higher order partial derivatives for integral of the Bochner-Martinelli type on a closed smooth manifold ∂D in Cn. From the Plemelj formulas and using the theory of complex partial differential equation, we prove that the problem of higher order boundary value DκΦ+(t) = DκΦ−(t) + f(t) is equivalent to a complex linear higher order partial differential equation. Moreover, given a proper condition of the Cauchy boundary value problem, the problem of higher order boundary value has a unique branch complex harmonic solution satisfying Φ−(∞) = 0 in Cn\∂D. 相似文献