A NOTE ON THE NULLITY OF HOMOTOPY GROUP FOR COMPLETE THREE DIMENSIONAL MANIFOLDS WITH RICCI ≧ 0

This note shows the nullity of homotopy groups for complete three dimensional manifoldswith Ricci≥ 0 under some growth condition of the geodesic ball. The author also gives someexamples which show the growth condition here is optimal in some sense.     

ON THE EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR A CLASSOF DEGENERATE ELLIPTIC SYSTEMS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＳＹＳＴＥＭＳ￥ＣＨＥＮＺＨＥＮＴＡＯ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｘｉａｎｇｔ...     

CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

A class of second order nonlinear differential equations with delay depengingon the unknown function of the from(r(t)ψ(x(t))x' (t))' f (t, x(t), x (△ (t, x(t)))) = 0in the case where ∫∞0 ds/r(s) ＜∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.     

FATOU PROPERTY ON HARMONIC MAPS FROM COMPLETE MANIFOLDS WITH NONNEGATIVE CURVATURE AT INFINITY INTO CONVEX BALLS

ＦＡＴＯＵＰＲＯＰＥＲＴＹＯＮＨＡＲＭＯＮＩＣＭＡＰＳＦＲＯＭＣＯＭＰＬＥＴＥＭＡＮＩＦＯＬＤＳＷＩＴＨＮＯＮＮＥＧＡＴＩＶＥＣＵＲＶＡＴＵＲＥＡＴＩＮＦＩＮＩＴＹＩＮＴＯＣＯＮＶＥＸＢＡＬＬＳ￥ＹＡＮＧＹＩＨＵＡｂｓｔｒａｃｔ：Ｔｈｅａｕｔｈｏｒｃ...     

ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G（2,5）

In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G(2, 5) with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ : S2 → G(2, 5) is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.     

ON THE FUNDAMENTAL GROUP OF OPEN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE＊＊＊＊

The authors establish some uniform estimates for the distance to halfway points of minimal geodesics in terms of the distantce to end points on some types of Riemannian manifolds, and then prove some theorems about the finite generation of fundamental group of Riemannian manifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.     

THE SOLUTION OF b的偏导-EQUATION OF （P,Q）-FORMS AND IT′ S L^p ＆ HOLDER ESTIMATES ON A STEIN MANIFOLD

By using the kernel of J. P. Demaily &;amp; Laurrent Thiebaut, the author constructs two opertors T and S which are compact and obtain the solution of b的偏导-equation of (p,q)forms and L &;amp; Holder estimates on a Stein Manifold.     

ON THE EXISTENCE,MULTIPLICITY AND UNIQUENESS OF POSITIVE SOLUTION FOR A THIRD ORDER TWO-POINT BOUNDARY VALUE PROBLEM

The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.     

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATION WITH CONVEX AND CONCAVE NONLINEARITIES

In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.     

ON EQUILIBRIA AND PERIODIC ORBITS OF COOPERATIVE SYSTEMS IN R~3

In the paper we present new criteria for existence of equilibria and periodic orbits for 3-dimensional systems which are cooperative. Particular attention is given to the relations of equilibria, cycle K and stable manifold of K. Meanwhile, the results of Hirsch [1, Theorem 9] and Jiang [2] are improved.     

CONFORMAL DEFORMATION OF COMPLETE SURFACE WITH NEGATIVE CURVATURE

ＣＯＮＦＯＲＭＡＬＤＥＦＯＲＭＡＴＩＯＮＯＦＣＯＭＰＬＥＴＥＳＵＲＦＡＣＥＷＩＴＨＮＥＧＡＴＩＶＥＣＵＲＶＡＴＵＲＥＺＨＯＵＤＥＴＡＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ３１,１９９４．ＲｅｖｉｓｅｄＡｕｇｕｓｔ３０,１９９５．Ｄ...     

BOUNDEDNESS OF POSITIVE SOLUTIONS OF THE CONFORMAL SCALAR CURVATURE EQUATION AND POSITIVE SCALAR CURVATURE

We study the boundedness of positive solutions of the conformal scalar curvature equation in a complete Riemannian manifold, in connection with conformal metrics of strictly positive scalar curvature.     

具有非负Ricci曲率和次大体积增长的完备流形(英文)

本文研究了具有非负Ricci曲率和次大体积增长的完备黎曼流形的拓扑结构问题.利用Toponogov型比较定理及临界点理论,获得了流形具有有限拓扑型的结果,推广了H.Zhan和Z.Shen的定理,并且还证明了该流形的基本群是有限生成的.     

THEOREMS OF BARTH-LEFSCHETZ TYPE ON KAHLER MANIFOLDS WITH PARTIALLY POSITIVE CURVATURE

The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given.     

DARBOUXEQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIAN MANIFOLDS WITHNONNEGATIVE CURVATURE INR

50.IntroductionAsDarbouxpointedout,theisometricembeddingoftwodimensionalRiemannianmanifoldsinR3leadstosolveanonlinearpartialdifferentialequationofMongeAmperetypewhereVZz=(iii--r;zk)denotestheHessianofzwithrespecttothegivensmoothmetricg=gijdu'duidefinedonfi,g'Jtheinverseofthemetrictensorandkthecurvatureofthemetricg.Indeed,fromtheGaussequationsoftherequiredisometricembedding/~(x,igz),wherefitjarethecoefficientsofitssecondfundamentalformandacisitsnormal,computingtheinnerproductsofthelastexpre…     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.     

半线性椭圆方程正解存在性

本文讨论了临界指数情形半线性椭圆方程-Δu+α(x)u=b(x)u~p+g(x,u)在R~n中的正解存在性。     

COMPLETE HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A SPECIAL KIND OF LOCALLY SYMMETRIC MANIFOLD

In this paper, we investigate n-dimensional complete and orientable hypersufaces M n (n ≥ 3) with constant normalized scalar curvature in a locally symmetric manifold. Two rigidity theorems are obtained for these hypersurfaces.     

EXISTENCE OF POSITIVE RADIAL SOLUTIONS AND ENTIRE SOLUTIONS FOR QUASILINEAR SINGULAR BOUNDARY VALUE PROBLEMS

ＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＲＡＤＩＡＬＳＯＬＵＴＩＯＮＳＡＮＤＥＮＴＩＲＥＳＯＬＵＴＩＯＮＳＦＯＲＱＵＡＳＩＬＩＮＥＡＲＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＹａｎｇＺｕｏｄｏｎｇ（杨作东）＆ＧｕｏＺｏｎｇｍｉｎｇ（郭...