共查询到20条相似文献,搜索用时 78 毫秒
1.
2.
3.
从对偶矢量入手.在剖析函数微分内在涵义的基础上,由具体至抽象地引入微分1-形式.进而通过外乘法与外微分运算,引进高阶微分形式;通过介绍微分形式的积分转换方法,自然过渡到Stokes定理;最后通过微分形式在矢量分析中的应用,将抽象的理论回归到具体工程计算.由此实现微分形式的教学过程。 相似文献
4.
<正> 古典的 Liouville 定理说:全平面上有界的全纯函数必是常数.在多复变函数论里,有许多定理是研究什么样的复流形上不存在非常值或非退化的(有界)全纯函数或全纯映照.这类定理可以统称为 Liouville 型定理.与一个复变数情况不同的是这类定理大多可以由复流形上的 Schwarz 引理推出.例如,S.T.Yau 证明了一个 Schwarz 引理后 相似文献
5.
李娟 《数学物理学报(A辑)》2007,27(3):515-523
该文证明了满足A -调和方程的微分形式的局部双权积分不等式. 作为局部结果的应用,还证明了满足A -调和方程的微分形式的整体双权积分不等式. 相似文献
6.
7.
8.
为了帮助学生正确理解微分形式不变性的本质,主张教师应在相关教学中注重加强建立形式与内容之间的联系,深入阐释形式化符号表达的巧妙,并培养学生积极调用数学经验与数学直觉来解决有关问题. 相似文献
9.
证明微分形式的局部加权积分不等式,然后通过利用局部的结果,分别地在 Ls(μ)-平均域和John域上证明了微分形式的整体加权积分不等式,这可以认为是经 典的Poincaré型不等式的推广. 相似文献
10.
11.
Kichenassamy found conditions under which the space W
p
k
of differential forms on a closed manifold M embeds compactly in the space F
p
k
of currents on M. We give a version of Kichenassamy's theorem for an arbitrary Banach complex and, in particular, for an elliptic differential complex on a closed manifold. 相似文献
12.
Let : M N be a harmonic morphism from a complete noncompact Riemannian manifold M with nonnegative Ricci curvature to a complete Riemannian manifold N with nonpositive scalar curvature. We show if the energy of is finite, then is constant. This can be compared with a similar result for harmonic maps when N has nonpositive sectional curvature due to Schoen and Yau. 相似文献
13.
考虑对角型椭圆组=f_i(x,u,(?)u),i=1,2,…,N. 对一种特殊情形证明其广义解的Liouville型定理成立. 相似文献
14.
In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if : MNis a p-harmonic morphism (p2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E
p
(), or (2p–2)-energy E
2p–2() is finite, then is constant. 相似文献
15.
16.
Micah Warren 《偏微分方程通讯》2013,38(5):922-932
We derive a Liouville type result for special Lagrangian equations with certain “convexity” and restricted linear growth assumptions on the solutions. 相似文献
17.
Consider a real-analytic orientable connected complete Riemannian manifold M with boundary of dimension n ≥ 2 and let k be an integer 1 ≤ k ≤ n. In the case when M is compact of dimension n ≥ 3, we show that the manifold and the metric on it can be reconstructed, up to an isometry, from the set of the Cauchy data for harmonic k-forms, given on an open subset of the boundary. This extends a result of [14] when k = 0. In the two-dimensional case, the same conclusion is obtained when considering the set of the Cauchy data for harmonic 1-forms. Under additional assumptions on the curvature of the manifold, we carry out the same program when M is complete non-compact. In the case n ≥ 3, this generalizes the results of [13] when k = 0. In the two-dimensional case, we are able to reconstruct the manifold from the set of the Cauchy data for harmonic 1-forms. 相似文献
18.
Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed. 相似文献
19.
A. G. Aleksandrov 《Functional Analysis and Its Applications》2005,39(4):245-255
We introduce the notion of logarithmic index of a vector field on a hypersurface and prove that the homological index can be expressed via the logarithmic index. Then both invariants are described in terms of logarithmic differential forms for Saito free divisors, which are hypersurfaces with nonisolated singularities, and all contracting homology groups of the complex of regular holomorphic forms on such a hypersurface are computed. In conclusion, we consider the case of normal hypersurfaces, including the case of an isolated singularity, and describe the contracting homology of the complex of regular meromorphic forms with the help of the residue of logarithmic forms. 相似文献
20.
本文研究上半空间一类含有多调和延拓算子的积分方程组正解的分类问题.在某些自然结构假设下,利用积分形式的移动球面法和上半空间的积分不等式,获得了该积分方程组正解的Liouville型定理,推广了已有的结果. 相似文献