Blow—up of Solutions of Heat Flows for Harmonic Maps

Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)相似文献   

扰动非线性Schroedinger方程组的动力性态

研究具周期边界条件的扰动非线性Schroedinger方程组的动力性态，首先，在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析，然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性．     

宇宙常数的Bulk流形的起源

关于宇宙常数问题是个至今没有解决的问题, 它的来源至今还没有一个共识. 从额外维的流形出发, 给出了宇宙常数的,bulk,流形起源的理论, 得到了不同情况下宇宙常数的取值和宇宙常数随时间演化的函数, 并且得到了可拟合现代天文观测的宇宙常数.     

Poisson流形上微缩算子η的应用

本文根据Poisson流形P的1-形式空间∧1(P)上的微缩算子η及其性质,给出了η-代数胚的定义,进一步得到了微缩算子在η-代数胚及Poisson流形中的一些应用.     

可微变换在不动流形处的局部标准化

变换在不动点处的局部线性化问题,当不动点是孤立点的情况,已经得到了详尽的研究。对于变换的不动点集合成为子流形的情况,在文献中还很少见到。本文用流形的横截性质讨论R~n中具有(n-k)维不动流形的可微变换,给出了变换的局部等价的线性化标准形式。     

从具体例子看惯性流形概念的推广

惯性流形的概念要求所有轨道指数收敛于唯一吸引子[5],这对于很多物理问题,例如sine-Gordon方程是很难满足的[4],本文中给出的人工例子建议了惯性流形的推广形式,这个推广形式去掉了整体吸引子是唯一的预先要求,该推广概念使用于sine-Gordon方程。     

THE MAIN INVARIANTS OF A COMPLEX FINSLER SPACE

In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwald frame. The geometry of such manifolds is controlled by three real invariants which live on T ′M : two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular interest. Complex Berwald spaces coincide with K¨ahler spaces, in the two-dimensional case. We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the K¨ahler purely Hermitian spaces by the fact K = W = constant and I = 0. For the class of complex Berwald spaces we have K = W = 0.Finally, a classification of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.     

LIMIT CYCLES BIFURCATION FOR A CLASS OF DEGENERATE SINGULARITY

In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new.     

Projective vector fields on Finsler manifolds

In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.     

关于SOL流形具有常平均曲率旋转曲面的注记

研究非欧流形SOL 空间上共形平均曲率方程的可解性,通过研究轮廓曲线对具有平均曲率的旋转曲面进行分类。当这些旋转曲面的平均曲率为给定函数时,计算出相应轮廓曲线的微分方程。通过求解这些微分方程,给出旋转函数是其上共形平均曲率的充分条件。