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Immortal solution of the Ricci flow

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Science China Mathematics 2005年第Z1期48卷 217-224页

作者： RUAN Qihua & CHEN Zhihua Department of Applied Mathematics, Tongji University, Shanghai 200092, China Department of Mathematics, Putian College, Putian 351100, China Department of Applied Mathematics Tongji University Shanghai China Department of Mathematics Putian College Putian China

For any complete noncompact Kahler manifold with nonnegative and bounded holomorphic bisectional curvature. we provide the necessary and sufficient condition for the immortal solution to the Ricci flow.

关键词： Ricci flow, immortal solution, holomorphic bisectional curvature.

Some projectively flat (α,β)-metrics

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Science China Mathematics 2006年第6期49卷 838-851页

作者： SHEN Yibing ZHAO Lili Department of Mathematics Zhejiang University Hangzhou 310028 China Department of Mathematics Zhejiang University Hangzhou 310028 China

In this paper, we study a class of Finsler metrics in the form F = α + ∈β + 2k β2/α-k2β4/3α3 , where α= (√aijyiyj) is a Riemannian metric, β = biyi is a 1-form, and ∈ and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature.must be locally Minkowskian.

关键词： projectively flat, Finsler (α, β)-metrics, flag curvature.

Geometric aspects of the moduli space of Riemann surfaces

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Science China Mathematics 2005年第Z1期48卷 97-122页

作者： Shing-Tung Yau Department of Mathematics Harvard University CambridgeMA 02138USA

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature.properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore,the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.

关键词： moduli space, Teichmuller space, metric, curvature.

Conformal minimal two-spheres with constant Gauss curvature.in U(3)

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Chinese Science Bulletin 1998年第12期43卷 994-997页

作者： Jiao Xiaoxiang Peng Jiagui Univ Sci & Technol China Grad Sch Dept Math Beijing 100039 Peoples R China

A complete classification of all conformal minimal 2-sphere with constant Gauss curvature.is given in U(3).

关键词： conformal minimal Gauss curvature.

ON ASYMPTOTICS RELATED TO THE STATISTICAL curvature. IN NONLINEAR REGRESSION

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Chinese Science Bulletin 1990年第14期35卷 1165-1168页

作者：韦博成 Department of Mathematics Southeast University Nanjing 210018 PRC

Efron, Hinkley and Amari have studied several asymptotic properties related to the statistical curvature. for a specific curved exponential family in which the samples are independent and identically distributed and the curvature. are defined in a fixed space. In this note, we study the similar asymptotics for nonlinear regression, but there are two substantial differences from the family studied by Efron and Amari. First,

关键词： nonlinear regression statistical curvature.

Schrdinger flow of maps into symplectic manifolds

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Science China Mathematics 1998年第7期41卷 746-755页

作者：丁伟岳王友德

The definition of Schrdinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrdinger flow of maps into S 2, and that there exists a unique local smooth solution for the initial value problem of one dimensional Schrdinger flow of maps into Khler manifolds. In case the targets are Khler manifolds with constant curvature. it is proved that one dimensional Schrdinger flow admits a unique global smooth solution.

关键词： Schr dinger flow K hler manifold conservative law sectional curvature.

ESTIMATES OF THE FIRST EIGENVALUE FOR A COMPACT RIEMANN MANIFOLD

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Science China Mathematics 1990年第1期33卷 39-51页

作者：杨洪苍 Institute of Mathematics Sciences Acadamia Sinica

This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature.-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eig... 详细信息

关键词： Riemann manifold eigenvalue Ricci curvature.