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General expansion for period maps of Riemann surfaces

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Science china Mathematics 2010年第8期53卷 2021-2030页

作者： YIN FangLiang center of mathematical sciences,zhejiang university,hangzhou 310027,china 1. center of mathematical sciences Zhejiang University Hangzhou 310027 China

In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers *** generalizes fully the famous Rauch's variational *** applications,we compute the curvature of Siegel metric at point [X] with Π([X]) =√ -1 Ig and the Christoffel symbols of L2-induced Bergman metric on Mg.

关键词： period map moduli space Siegel metric Bergman metric

TRIPLE　INTERACTIONS　OF　CONORMAL　WAVES　FOR　HIGHER　ORDER　SEMILINEAR　HYPERBOLIC　EQUMIONS

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 23-32页

作者： FANG DAOYUAN (center for mathematical sciences, zhejiang university, hangzhou 310027, china.) 浙江大学数学科学中心浙江杭州

The interaction of three conormal waves for semi-linear strictly hyperbolic equations of third order is considered. Let Σi, i = 1, 2, 3, be smooth characteristic surfaces for P= Da(D_t￣2 -△) intersecting transversally at the origin. Suppose that the solution u to Pu = f(t, x ,y)D u), ≤2 is conormal to Σi, i = 1, 2, 3, for t < 0. The author uses Bony's second microlocajization techniques and commutator arguments to conclude that the new singularities a short time after the triple interaction lie on the surface of the light cone Γ over the origin plus the surfaces obtained by flow-outs of the lines of intersection Γ ∩ Σi and Σi∩ Σj, i, j = 1, 2, 3.

关键词： Hyperbolic equation Conormal wave Interaction Characteristic surface.

Complete hypersurfaces in a 4-dimensional hyperbolic space

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 370-378页

作者： XU Hong-wei1 ZHAO En-tao2 center of mathematical sciences,zhejiang university,hangzhou 310027,china center of mathematical sciences Zhejiang University Hangzhou 310027 China

This paper gives a classification of complete hypersurfaces with nonzero constant mean curvature and constant quasi-Gauss-Kronecker curvature in the hyperbolic space H4（-1）,whose scalar curvature is bounded from below.

关键词： complete hypersurface mean curvature quasi-Gauss-Kronecker curvature

Lipschitz continuity of best approximations and Chebyshev centers

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Chinese Science Bulletin 1998年第3期43卷 185-188页

作者： LI Chong 1 and WANG Xinghua 2 1. center for mathematical sciences, zhejiang university, hangzhou 310027, china 2. Department of Mathematics, hangzhou university, hangzhou 310028, china center for mathematical sciences Zhejiang University Hangzhou China Department of Mathematics Hangzhou University Hangzhou China

The Lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.

关键词： best approximation Chebyshev center uniform convexity.

On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators

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Acta Mathematica Sinica,English Series 1994年第3期10卷 315-324页

作者： Chen Dirong Department of Mathematics Beijing Normal university Beijing,100875 and center for mathematical sciences zhejiang university hangzhou,310027 china 1. Department of Mathematics Beijing Normal University 100875 Beijing 2. center for mathematical sciences Zhejiang University 310027 Hangzhou China

This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential *** remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF ***,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.

关键词： Math On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators lim Chen 卜成

EMBEDDED 2-SPHERES IN INDEFINITE 4-MANIFOLDS

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 257-262页

作者： GAN DANYAN(Depedmellt of Mathematics and center for mathematical sciences, zhejiang university hangzhou310027, china.)(Project supported by the National Natural Science Foundation of china and by the zhejiang NaturalScience Foundation.) zhejiang UNIV DEPT MATHHANGZHOU 310027PEOPLES R CHINA zhejiang UNIV CTR MATH SCIHANGZHOU 310027PEOPLES R CHINA

The main results are as *** be an element of H2, where γ, δ1,…δn. arestandard generators. Suppose2≤n≤9.(1) If for some i and some i, then ζ can be represented by a smoothly embedded 2-sphere.(2) If ζ is a characteristic homology class, then ζ cannot be represented by a smoothlyembedded 2-sphere except for ζ2 = 16l+1 - n, l = 0 and (3) If ζ= dη for some d∈Z, where η is a primitive ordinary homology class with η2 = 0,then ζ is eqivalent to (d; d, 0,..., 0) and can be represented by a smoothly embedded 2-sphere.

关键词： Representing Characteristic Ordinary Primitive

On a class of weak Landsberg metrics

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Science china Mathematics 2007年第4期50卷 573-589页

作者： Ben-ling LI & Zhong-min SHEN Department of Mathematics, zhejiang university, hangzhou 310028, china Department of mathematical sciences, Indiana university Purdue university Indianapolis (IUPUI), 402 N. Blackford Street, Indianapolis, IN 46202-3216, USA center of mathematical sciences, zhejiang university, hangzhou 310027, china 1. Department of Mathematics Zhejiang University Hangzhou 310028 China 2. Department of mathematical sciences Indiana University Purdue University Indianapolis (IUPUI) 402 N. Blackford Street Indianapolis IN 46202-3216 USA 3. center of mathematical sciences Zhejiang University Hangzhou 310027 China

In this paper, we discuss a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We characterize weak Landsberg metrics in this class and show that there exist weak Landsberg metrics whi... 详细信息

关键词： Finsler metric weak Landsberg metric (α,β)-metric 53B40

Behaviour of an Oscillatory Singular Integral on Weighted Local Hardy Spaces

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Acta Mathematica Sinica,English Series 1997年第3期13卷 305-320页

作者： Chen Liyuan (Department of Economics,Hangszhou university,hangzhou 310028,china)Sun Qiyu (center for mathematical sciences,zhejiang university,hangzhou 310027,china) Department of Economics Hangszhou University center for mathematical sciences Zhejiang University

The boundedness on weighted local Hardy spaces h1,pw of the oscillatory singular integral Tf（x）=∫Rn eiQ（x,y）K（x,y）f（y）dy is considered when Q（x,y）=P（x-y）for some real-valued polynomial P with its degree not less than *** a sufficient and necessary condition on polynomial Q on Rn × Rn such that T maps h1,pw to the weighted integrable function space L1w is found.

关键词： Oscillatory singular integral Weighted local Hardy spaces Muckenhoupt weight

GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD

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Acta Mathematica Scientia 2007年第3期27卷 611-618页

作者：谢纳庆许洪伟 Institute of Mathematics Fudan University center of mathematical sciences Zhejiang University

This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.

关键词： Submanifolds second fundamental form pinched Riemannian manifold