A Pinching Theorem for Minimal Submanifolds in Sphere

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单位球面中极小子流形的曲率拼挤

本文证明了单位球面中极小子流形的一些拼挤定理,特别注意到单位球面中的极小超曲面、给出了截曲率的拼挤常数,我们也改进了由Ｎ．Ｅｊｉｒｉ得到的Ｒｉｃｃｉ曲率拼挤常数。     

一类双调和方程的可解性

利用上下解方法、嵌入定理和Leray-schauder不动点定理证明了一类双调和方程弱解的存在性定理.做为定理的应用,给出了一个实例.     

一类双调和方程弱解的存在性研究

利用上下解方法、嵌入定理和Leray-Schauder不动点定理证明了一类双调和方程弱解的存在性定理.做为定理的应用,给出了一个实例.     

Solvability of a Mixed Problem with Nonlinear Boundary Condition for a One-Dimensional Semilinear Wave Equation

Mathematical Notes - For a one-dimensional semilinear wave equation, a mixed problem with nonlinear boundary condition is considered. The uniqueness and the local and global solvability of the...     

Lewy方程的局部可解性问题

本文引入一种关于部分变数为空间,关于部分变数为整函数空间Z的所谓F_(DZ)空间,利用富氏变换方法,找出Lewy方程在这种基本空间的对偶空间中解的表达式注1)。 一、Lewy方程的形式基本解 先从形式的运算出发。 关于x_3作富氏变换:     

基于拟常曲率度量的拟DeTurck流的稳定性

C.Guenther利用中心流形以及极大正规性原理,讨论了常曲率空间中DeTurck流的稳定性问题.将常曲率空间推广为拟常曲率空间并讨论"拟"DeTurck流的稳定性问题,得到类似于C.Guenther所得的结果.     

单位球面上的子流形有关截曲率的Pinching定理

设M是单位球面上不含脐点的子流形,Moebius形式Φ消失,本文讨论M 关于Mobius度量的截曲率的Pinching问题.     

关于局部对称空间中极小子流形的一个Ricci曲率pinching定理

研究局部对称空间中具有正Ricci曲率的完备极小子流形,得到了关于子流形Ricci曲率的一个pinching定理,把Norio Ejiri的结论从外围空间为球空间推广到局部对称空间中。     

Kaup-Kupershmidt方程Cauchy问题的局部可解性

This paper deals with the local solvability of initial value problem for Kaup-Kupershmidt equations. Indeed, using Bourgain method, we prove that the Cauchy problem of Kaup-Kupershmidt equation is local well-posed in H8 whenever s 〉 9/8, which improves the former results in [5].     

Examples of Hermitian Manifolds with Pointwise Constant Holomorphic Sectional Curvature

We construct non-compact examples of Hermitian manifolds with pointwise constant holomorphic sectional curvature. Our examples are obtained by conformal change of the metric on an open set of the complex space form.     

具有边界摄动的抛物型方程的可解性

本文研究了具有边界摄动的抛物型方程.利用可解性的讨论,得到了原问题的摄动解.     

Solvability,Structure, and Analysis for Minimal Parabolic Subgroups

We examine the structure of the Levi component MA in a minimal parabolic subgroup \(P = MAN\) of a real reductive Lie group G and work out the cases where M is metabelian, equivalently where \(\mathfrak {p}\) is solvable. When G is a linear group we verify that \(\mathfrak {p}\) is solvable if and only if M is commutative. In the general case M is abelian modulo the center \(Z_G\) , we indicate the exact structure of M and P, and we work out the precise Plancherel Theorem and Fourier Inversion Formulae. This lays the groundwork for comparing tempered representations of G with those induced from generic representations of P.     

局部对称共形平坦黎曼流形中紧致极小子流形的一个刚性定理

本文研究局部对称共形平坦黎曼流形中紧致极小子流形,得到了这类子流形第二基本形式模长平方关于外围空间Ricci曲率的—个拼挤定理,推广了文[1]中的结果.     

On the Solvability of a Mixed Problem for an One-dimensional Semilinear Wave Equation with a Nonlinear Boundary Condition

In this paper, for an one-dimensional semilinear wave equation we study a mixed problem with a nonlinear boundary condition. The questions of uniqueness and existence of global and blow-up solutions of this problem are investigated, depending on the nonlinearity nature appearing both in the equation and in the boundary condition.     

半李普希兹算子方程的逼近可解性

本文先在（π）1空间的闭集上证明了凝聚映射必为A-proper映射,运用此性质证明了型如f（x）-λx=0方程当f为弱内向、半李普希兹映射时是弱逼近可解的,若f为李普希兹型映射,方程还是强逼近可解的.     

On Solvability of Nonlocal Problem for Loaded Parabolic-Hyperbolic Equation

We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains the partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville of values of function derivative on the degeneration line and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.     

一类二阶隐式微分方程的可解性

本文关注如下的二阶隐式微分方程f（t，u（t），u″（t））=0，a．e．t∈（O，1），边值条件为u（0）=u（1）=0．利用上下解方法和迭代技巧研究了该问题的可解性并得到了一些解的存在性结果．