Ergodic measures of geodesic flows on compact Lie groups

Let Ψ be the geodesic flow associated with a two-sided invariant metric on a compact Lie group. In this paper, we prove that every ergodic measure μ of Ψ is supported on the unit tangent bundle of a flat torus. As an application, all Lyapunov exponents of μ are zero hence μ is not hyperbolic. Our underlying manifolds have nonnegative curvature (possibly strictly positive on some sections), whereas in contrast, all geodesic flows related to negative curvature are Anosov hence every ergodic measure is hyperbolic.     

完备非紧具非负曲率流形之拓扑结构

本文给出完备非紧具非负曲率的Ｒｉｅｍａｎｎ流形具有限拓扑型的一个简单证明     

DARBOUX EQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIAN MANIFOLDS WITH NONNEGATIVE CURVATURE IN R^3

The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate on the boundary is contained. As some applications the smooth isometric embeddings of positively and nonnegatively curved disks into Rs are constructed.     

完备非紧具非负曲率流形之拓扑结构

本文给出完备非紧具非负曲率的Riemann流形具有限拓扑型的一个简单证明.     

以0≤K∈C0∞为Gauss曲率的曲面的正则性

在较弱的条件下 ,证明了以给定的具有紧支集的非负函数为Gauss曲率 ,以已知的空间曲线为边界的凸曲面是整体C^1,1的 .有例子表明这个正则性是最佳的.     

Generalized Liouville Theorem in Nonnegatively Curved Alexandrov Spaces

In this paper, Yau＇s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.     

具非负曲率完备非紧曲面的几何性质

本文证明了单连通完备非紧具非负曲率之曲面的任一测地线γ：[0，+∞)→M均趋于∞处这一几何性质，指出了一般的高维流形不具有此性质.本文还证明了单连通完备非紧具非负曲率的曲面的割迹与第一共轭轭迹是一致的；并且讨论了一般高维流形的共轭点与测地线的关系.