Existence and bifurcation of integral manifolds with applications

In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.     

向量场的奇点集与陈数(英文)

在此文中,我们给出一个紧致复m维Hermite流形的陈数的几何解释,用定义在M上的向量场的奇点集去表示陈数。     

An Estimate for a Fundamental Solution of a Parabolic Equation with Drift on a Riemannian Manifold

We construct a fundamental solution for a parabolic equation with drift on a Riemannian manifold of nonpositive curvature. We obtain some estimates for this fundamental solution that depend on the conditions on the drift field.     

Uniform energy decay of Schrodinger equations with variable coefficients

This paper establishes the exponential decay of the solutionsof the Schrödinger equation with variable coefficientsin the principal part subject to dissipative feedback actingin the Dirichlet boundary condition. The approach adopted usesa lifting argument in the topology of the solution along withRiemannian geometry method.     

Hermite流形上Coupled Vortex方程的Dirichlet问题

本文研究Coupled Vortex方程的Dirichlet问题,通过热流方法来讨论该方程Dirichlet问题的解的存在唯一性．     

Théorème de séparation de type Andreotti–Vesentini sur les variétés CR

We give an Andreotti–Vesentini separation theorem on q-concave at infinity CR submanifolds. Mathematics Subject Classification (2000) 32V20, 32F10 Mots-clés: q-concave· variété CR·théorème de séparation·q-concave à l’infini     

拟周期时滞耗散半线性波方程的惯性流形

本文研究了具有拟周期外力作用的时滞波方程解的长时间性态,利用斜积半流方法,在扩展相空间中将非自治系统提升成自治系统,利用算子半群理论及Lyapunov-Perron方法在一定的谱间隙条件和充分小的时滞假设下,证明了拟周期半线性时滞波方程惯性流形的存在性.     

Some algebraic examples of Frobenius manifolds

Using analytic methods of finite-gap integration, we construct quasihomogeneous algebraic solutions of the WDVV associativity equations and the nonsemisimple Frobenius manifolds associated with them. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 195–206, May, 2007.     

Isometric Actions of Heisenberg Groups on Compact Lorentz Manifolds

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-analytic.