非负曲率流形上的丛

本文主要证明了射影空间乃至齐性空间上各种向量丛的全空间可以赋予截面曲率非负的完备度量。     

曲率渐近非负流形

本文主要研究了在曲率渐近非负流形上的一些性质：其上不存在非常数的正调和函数；若其调和函数是对一固定指数d的多项式增长,那么由这些调和函数所组成的空间的维数≤Cd~(CD),而且此流形的体积为无穷大等．     

曲率渐近非负流形

本文主要研究了在曲率渐近非负流形上的一些性质其上不存在非常数的正调和函数;若其调和函数是对一固定指数d的多项式增长,那么由这些调和函数所组成的空间的维数≤CdCD,而且此流形的体积为无穷大等.     

非负Ricci曲率开流形的拓扑

我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.     

关于四元射影空间的正曲率全复子流形

本文讨论四元射影空间的全复子流形，证明了四元射影空间的正截面曲率紧致全复子流形一定是全测地的。     

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     

R^n空间上具有正曲率和负曲率的度量一些例子

From the class of conformally flat metric of gij=f(|x|^2)δij defined on R^n,where f:[0,∞]→（0,∞）is a C^2 function,we find one class of metrics with positive curvature and two classes of complete metrics with negative curvature.     

负曲率流形上给定数量曲率的共形形变

本文研究具强负曲率Cartan－Hadamard流形M~n（n≥3）上给定数量曲率函数S的共形形变问题．利用上下解方法,并通过精心构造上解,我们获得了当完备的共形形变度量存在时,函数S在无穷远附近的最佳渐近性态．在较一般情况下,我们还给出了共形数量曲率方程解的渐近估计．     

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.     

具有调和曲率与有限$L^p$曲率的完备流形

Let(M~n, g)(n ≥ 3) be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R?m the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R?m goes to zero uniformly at infinity if for p ≥ n, the L~p-norm of R?m is finite.As applications, we prove that(M~n, g) is compact if the L~p-norm of R?m is finite and R is positive, and(M~n, g) is scalar flat if(M~n, g) is a complete noncompact manifold with nonnegative scalar curvature and finite L~p-norm of R?m. We prove that(M~n, g) is isometric to a spherical space form if for p ≥n/2, the L~p-norm of R?m is sufficiently small and R is positive.In particular, we prove that(M~n, g) is isometric to a spherical space form if for p ≥ n, R is positive and the L~p-norm of R?m is pinched in [0, C), where C is an explicit positive constant depending only on n, p, R and the Yamabe constant.     

HERMITIAN-EINSTEIN METRICS FOR HIGGS BUNDLES OVER COMPLETE HERMITIAN MANIFOLDS

In this paper, we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds. Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a class of complete Hermitian manifolds.     

POSITIVELY CURVED COMPLETE NONCOMPACT KAHLER MANIFOLDS

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. Among other things, we prove that a complete noncompact Kahler surface with positive and bounded sectional curvature and with finite analytic Chern number c1（M）^2 is biholomorphic to C2.     

REGULARITY OF HARMONIC MAPS INTO POSITIVELY CURVED MANIFOLDS

Let M be a compact Riemannian manifold of dimension m, N a complete Amply connected δ-pinched Riemannian manifold of dimension n. There exists a constant d(n). It is proved that if m≤d(n), then every minimizing map from M into N is smooth in the interior of M. If m=d(n)+1, such a map has at most diserete singular set and in general the Hausdorff dimension of the singular set is at most m-d(n)-1.     

HARMONIC MAPS AND FUNDAMENTAL GROUPS OF NONPOSITIVELY CURVEDRIEMANNIAN MANIFOLDS

Ｔｈｅｔｈｅｏｒｙｏｆｈａｒｍｏｎｉｃｍａｐｓｉｎｔｏａｃｏｍｐａｃｔｎｏｎｐｏｓｉｔｉｖｅｌｙｃｕｒｖｅｄｔａｒｇｅｔｉｓｗｅｌｌ-ｄｅｖｅｌｏｐｅｄ.ＴｈｅｅｘｉｓｔｅｎｃｅｏｆｓｕｃｈａｈａｒｍｏｎｉｃｍａｐｐｉｎｇｉｎａｎｙｇｉｖｅｎｈｏｍｏｔｏｐｙｃｌａｓｓｉｓｅｓｔａｂｌｉｓｈｅｄｂｙＥｅｌｌｓａｎｄＳａｍｐｓｏｎ[1]ｉｎ1964,ａｎｄｌａｔｅｒ,ｉｎ1967,Ｈａｒｔｍａｎ[2]ｇａｖｅａｐｒｏｏｆｏｆｔｈｅｕｎｉｑｕｅｎｅｓｓ.Ｔｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏａｎａｐｐｌｉｃａｔｉｏｎｏ…     

一类Kahler 流形上的全纯映射

本文利用Kahler流形上的Laplace算子,给出了一类全纯映射的增长性结论.     

SOME RESULTS ON PRODUCT COMPLEX FINSLER MANIFOLDS

Let (M, F ) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M 1 , F 1 ) and (M 2 , F 2 ). In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γ i ; k associated to F and the Chern Finsler connection coefficients Γ a ; c , Γα ; γ associated to F 1 , F 2 , respectively. As applications we prove that, if both (M 1 , F 1 ) and (M 2 , F 2 ) are strongly Ka¨hler Finsler (complex Berwald, or locally complex Minkowski, respectively) manifolds, so does (M, F ). Furthermore, we prove that the holomorphic curvature K F = 0 if and only if K F1 = 0 and K F2 = 0.     

一类Kähler 流形上的全纯映射

本文利用Kahler流形上的Laplace算子,给出了一类全纯映射的增长性结论.     

WEAK TYPE(1,1)BOUNDEDNESS OF RIESZ TRANSFORM ON POSITIVELY CURVED MANIFOLDS

For complete Riemannian manifold M,it is proved that▽(-△)~(-1/2) is boundedfrom L~2(M)to weak-L~1(M)if Ric(M)≥0.     

VECTOR BUNDLES ON PROJECTIVE SPACES OVER A DISCRETE VALUATION RING

Let E be a vector bundle on P ⁿ _D, n ≥ 2, with D discrete valuation ring. Here we give a necessary and sufficient condition for the splitting of E as a direct sum of line bundles.