Stability of hyperbolic manifolds with cusps under Ricci flow

We show that every finite volume hyperbolic manifold of dimension greater than or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation.     

Lie algebroid modules and representations up to homotopy

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.     

H一射影循环Kaehler流形

本文研究H一射影循环Kaehler流形的性质，导出了该流形曲率张量的代数结构，从而深化了这类流形的已有结果。     

动物皮肤斑纹形成模式的数值模拟及定性分析

高级生物生命组织的形成机制是十分吸收人的课题，动物皮肤斑纹的变化和复杂性是其中的一个问题，文中对由活化质－基质和一个交换系统组成的系统，采用交替方向隐格式，进行了数值模拟，给出了二维和三维图像，其结果与长颈鹿的皮脸斑纹相符，用中心流形法，对系统的平衡点稳定性作了分析，原始数据条件下，其平衡点是稳定的，而当参数变化较大时，可能会发生突变。     

图式流形2n个顶点,n≥3的一个同胚分类定理

介绍计算缩影图式流形的同胚类的一个简单方法。     

Infinite-dimensional 4-manifold of finite cohomological dimension under the continuum hypothesis

Under the assumption of the continuum hypothesis, a differentiable 4-manifoldM of dimension dimM=∞ and cohomological dimension cA—dimM=4 is constructed. The spaceM is perfectly normal and hereditarily separable. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 664–670, November, 1999.     

流形P上向量场在余切丛T~*P上的拓展及有关讨论

本文先给出流形Ｐ上的向量场Ｃ在余切丛Ｔ＊Ｐ上拓展的表达式，继而给出Ｃ作用于或Ｃ受导子作用结果的三个命题．在此基础上，最后用公式给出关于拓展Ｔ＊（Ｃ）的性质的三个命题．     

Growth of heat trace and heat content asymptotic coefficients

We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their growth.     

Normal surfaces as combinatorial slicings

We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. Focus is given to the case of dimension 3, where slicings are (discrete) normal surfaces. For the cases of 2-neighborly 3-manifolds as well as quadrangulated slicings, lower bounds on the number of quadrilaterals of slicings depending on its genus g are presented. These are shown to be sharp for infinitely many values of g. Furthermore, we classify slicings of combinatorial 3-manifolds which are weakly neighborly polyhedral maps.     

R^n空间中闭光滑流形上的线性奇异积分方程

本文给出了高斯奇异积分的合成和反演公式,并且证明了R~n空间中闭光滑流形上的线性奇异积分方程的有关结果。