负曲率完备流形上方程△u=f的有界整体解

借助于Hessian比较定理和上下解方法，证明了对于相当多的一类非负函数f，负曲率完备黎曼流形上的方程△u=f都存在有界的整体解，从而刻画了这些黎曼流形的双曲性程度。     

局部$G$-凸一致空间上几乎不动点定理和不动点定理

得到局部G-凸一致空间上具有S-KKM性质的集值映射的新的几乎不动点定理和不动点定理.我们的结果对已有文献中的相应结论进行了改进和一般化.     

Almost Hermitian structures induced from a Kähler structure which has constant holomorphic sectional curvature

We obtain a non-Kähler almost Hermitian manifold of constant holomorphic sectional curvature by changing the almost complex structure in a Kähler manifold of constant holomorphic sectional curvature.

     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

On Some Ricci-Flat Metrics of Cohomogeneity Two on Complex Line Bundles

We construct a family of four-dimensional smooth Ricci-flat Riemann orbifolds of cohomogeneity two which possess the structure of complex line bundles.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

流形上随机流的渐近平坦性

本文的目的是讨论流形上由随机微分方程确定的扩散过程的体积零化性质。令X_t(x)是描述流形M上的微分同胚流x→X_t(x)的扩散过程,K是M中具有正有限Hausdorff测度的紧致曲面,我们给出X_t(K)的面积在t→∞时几乎必然趋于零的条件,特别地,随机流X_t(·)的渐近零化定向可求长弧r:[0,1]→M的弧长。     

The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits

We investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out.     

二阶Melnikov函数及其应用

在Ｍｅｌｎｉｋｏｖ函数的种种应用中，目前常见到的仅是一阶形式。本文具体推导了二阶Ｍｅｌｎｉｋｏｖ函数的分析表达，提出了临界情况下考察双曲鞍点的稳定流形与不稳定流形相对位置的二阶判据，并成功地用于环面ｖａｎｄｅｒＰｏｌ方程的研究中。     

Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.