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On mean curvatures in submanifolds geometry

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Science China Mathematics 2008年第6期51卷 1127-1134页

作者： GE JianQuan department of mathematical sciences,tsinghua university,beijing 100084,China department of mathematical sciences Tsinghua University Beijing China

By using moving frame theory,first we introduce 2p-th mean curvatures and(2p+1)-th mean curvature vector fields for a *** then give an integral expression of them that characterizes them as mean values of symmetric functions of principle *** we apply it to derive directly the celebrated Weyl-Gray tube formula in terms of integrals of the 2p-th mean curvatures and some Minkowski-type integral formulas.

关键词： moving frame mean curvature tube 5.A07 5.C42

On fixed-points and singular values of transcendental meromorphic functions

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Science China Mathematics 2010年第3期53卷 887-894页

作者： ZHENG JianHua department of mathematical sciences, tsinghua university, beijing 100084, China department of mathematical sciences Tsinghua University

In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for hyperbolic domains.

关键词： meromorphic functions fixed points singular points hyperbolic metric covering mapping

A Hierarchy of Multidimensional Hénon-Heiles Systems

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Acta Mathematica Sinica,English Series 2000年第3期16卷 527-534页

作者： Yunbo Zeng department of mathematical sciences,tsinghua university,beijing 100084 P.R.China department of mathematical sciences Tsinghua University Bejing 100084 P. R. China

A hierarchy of multidimensional Hénon-Heiles(M-H-H)systems are constructed via the x-and t_n-higher-order-constrained flows of KdV *** Lax representation for the M-H-H hierarchy is determined from the adjoint representation of the auxiliary linear problem for the KdV *** using the Lax representation the classical Poisson structure and r-matrix for the hierarchy are found and the Jacobi inversion problem for the hierarchy is constructed.

关键词： Higher-order constrained flow Multidimensional Hénon-Heiles systems Lax representation Jacobi inversion problem

Upper bound and formula for class numbers of abelian function fields

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Progress in Natural Science:Materials International 2006年第3期16卷 321-323页

作者： MA Lianrong and ZHANG Xianke (department of mathematical sciences, tsinghua university, beijing 100084, China) department of mathematical sciences Tsinghua University Beijing 100084 China

For any abelian function field K (i.e. any subfield of a cyclotomic function field L=k (∧P) over the rational function field k ) with conductor being an irreducible polynomial over a finite field of odd characteristic, by studying the Carlitz-module structure and the character group of K, an explicit upper bound and a calculating formula of the relative divisor class number h- (K) of K are given. Our calculated results of K develop Rosen’s recent results of L .

关键词： Carlitz module cyclotomic function field class number character abelian function field.

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

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Acta Mathematica Scientia 2008年第3期28卷 513-522页

作者：叶俊 department of mathematical sciences Tsinghua University

The purpose of this article is to obtain the quasi-stationary distributions of the δ（δ 〈 2）-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin （2001）. It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a （4 - δ）- dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.

关键词： Radial Ornstein-Uhlenbeck process quasi-stationary distribution quasiinvariant

Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds

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Science China Mathematics 2005年第5期48卷 618-648页

作者： LI Yuxiang department of mathematical sciences, tsinghua university, beijing 100084, China department of mathematical sciences Tsinghua University Beijing China

Let (M,g) be a compact Riemannian manifold without boundary, and (N,g) a compact Riemannian manifold with boundary. We will prove in this paper that the and can be attained. Our proof uses the blow-up analysis.

关键词： Moser-Trudinger inequality extremal function n-Lapalace Green function.

Heat kernel estimates on effective resistance metric spaces

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Progress in Natural Science:Materials International 2007年第7期17卷 775-783页

作者： Hu Jiaxin Ji Yuan Wen Zhiying (department of mathematical sciences,tsinghua university,beijing 100084,China) department of mathematical sciences Tsinghua University Beijing 100084 China

We obtain two-sided estimates of heat kernels on effective-resistance metric spaces by using an analytic *** applications,such as on post-critically finite self-similar sets and on products of effective resistance spa... 详细信息

关键词： Heat kernel effective resistance Dirichlet form Green’s function

Local Gromov-Witten invariants of canonical line bundles of toric surfaces

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Science China Mathematics 2010年第6期53卷 1571-1582页

作者： YANG Fei & ZHOU Jian department of mathematical sciences,tsinghua university,beijing 100084,China department of mathematical sciences Tsinghua University

We define and compute by localizating the local equivariant Gromov-Witten invariants of the canonical line bundles of toric surfaces,not necessarily Fano.

关键词： local Gromov-Witten invariants localization partition function geometric engineering

Unramified extensions of quadratic fields

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Progress in Natural Science:Materials International 2008年第3期18卷 323-324页

作者： Wei Li, Dong Yang, Xianke Zhang department of mathematical sciences, tsinghua university, beijing 100084, China department of mathematical sciences Tsinghua University Beijing 100084 China

Let K be a global quadratic field, then every unramified abelian extension of Kis proved to be absolutely Galois when Kis a number field or under some natural conditions when Kis a function field. The absolute Galois ... 详细信息

关键词： Global quadratic fields Unramified extensions