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On the rigidity theorem for harmonic functions in Khler metric of Bergman type

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Science China mathematics 2010年第3期53卷 779-790页

作者： LI Song-Ying 1,2, & WEI DongHuan 1 1 School of mathematics and Computer Science, Fujian Normal university, Fuzhou 350007, China 2 department of mathematics, university of california, irvine, ca 92697-3875, usa 1. School of mathematics and Computer Science Fujian Normal University Fuzhou 350007 China2. Department of Mathematics University of California Irvine CA 92697-3875 USA

The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these metrics u ( u h = 0) in B n , then h must be pluriharmonic in B n . In fact, it is a characterization theorem, as a consequence, the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails. The results in this paper generalize the theorems of Graham (1983) and examples constructed by Graham and Lee (1988).

关键词： rigidity pluriharmonic Laplace-Beltrami operators u-harmonic

POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 187-200页

作者： WAN DAQING(department of mathematics, university of california, irvine, ca 92697-3875, usa.) department of mathematics University of California Irvine CA 92697-3875 USA

A vanishing theorem is proved for e-adic cohomology with compact support on an affine (singular) complete intersection. As an application, it is shown that for an affine complete intersection defined over a finite field of q elements, the reciprocal "poles" of the zeta function are always divisible by q as algebraic integers. A p-adic proof is also given, which leads to further q-divisibiliy of the poles or equivalently an improvement of the polar part of the AxKatz theorem for an affine complete intersection. Similar results hold for a projective complete intersection.

关键词： Pole Zeta function Complete intersection

On characterizations of isometries on function spaces

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Science China mathematics 2008年第4期51卷 620-631页

作者： LI SongYing~(1+) RUAN YingBin~2 1 department of mathematics university of california irvine ca 92697 usa 2 School of mathematics and Computer Science Fujian Normal university Fuzhou 350007 China 1. department of mathematics University of California Irvine CA 92697 USA 2. School of mathematics and Computer Science Fujian Normal University Fuzhou 350007 China

The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball B n in ? n .

关键词： ismometry Besov spaces 32A17 47A15

ON THE KINEMATIC GEOMETRY OF MANY BODY SYSTEMS

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Chinese Annals of mathematics,Series B 1999年第1期20卷 11-28页

作者： WU-YI HSIANG(department of mathematics,university of california,berkeley,ca 94720-3840,usa) Univ calif Berkeley Dept Math Berkeley CA 94720 USA

In mechanics, both classical and quantum, one studies the profound interaction betweentwo types of energy, namely, the kinetic energy and the potential energy. The former can beorganized as the kinematic metric on the configuration space while the latter can be representedby a suitable potential function, such as the Newtonian potential in celestial mechanics andthe Coulomb potential in quantum mechanics of atomic and molecular physics. In this paper,the author studies the kinematic geometry of n-body systems. The main results are (i) theintroduction of a canonical coordinate svstem which reveals the total amount of kinematicsymmetry by an SO(3) x O(n-1) action in such a canonical coordinate representationt (ii) anin depth analysis of the above kinematic system both in the setting of classical invariant theoryand by the technique of equivariant Riemannian geometry; (iii) a remarkably simple formulafor the potential function in such a canonical coordinate system which reveals the well-fittingbetween the kinematic symmetry and the Potential energy.

关键词： Kinematic geometry Many body system Configuration space

Representations of Knot Groups and Twisted Alexander Polynomials

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Acta Mathematica Sinica,English Series 2001年第3期17卷 5+362-380页

作者： Xiao Song LIN department of mathematics,university of california,Riversides,ca 92521.usa department of mathematics University of California Riverside USA

We present a twisted version of the Alexander polynomial associated with a matrix rep- resentation of the knot *** of two knots with the same Alexander module but different twisted Alexander polynomials are given.

关键词： Twisted Alexander polynomial Representation space Knot group

Classification of rational holomorphic maps from B^2 into B^N with degree 2

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Science China mathematics 2009年第12期52卷 2647-2667页

作者： JI ShanYu 1 & ZHANG Yuan 2 1 department of mathematics, university of Houston, Houston, TX 77204, usa 2 department of mathematics, university of california at San Diego, La Jolla, ca 92093, usa department of mathematics University of Houston Houston USA department of mathematics Rutgers University New Brunswick USA

Rational proper holomorphic maps from the unit ball in C 2 into the unit ball C N with degree 2 are classified, up to automorphisms of balls.

关键词： rational holomorphic maps between balls classification maps with degree 2

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science China mathematics 2010年第3期53卷 719-738页

作者： KONG DeXing 1 , LIU KeFeng 2 & WANG YuZhu 3, 1 department of mathematics, Zhejiang university, Hangzhou 310027, China 2 department of mathematics, university of california at Los Angeles, ca 90095, usa 3 department of mathematics, Shanghai Jiao Tong university, Shanghai 200248, China 1. department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Department of Mathematics Shanghai Jiao Tong University Shanghai 200248 China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition cauchy problem smooth solution

Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2(R^d)

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Acta Mathematica Sinica,English Series 2005年第4期21卷 855-864页

作者： Zhi Hua ZHANG (Zhihua ZHANG) department of mathematics,university of california,Davis,california.95616,usa department of mathematics University of California Davis California 95616 USA

Let{ψμ} be an orthonormal wavelet of L^2（R^d） and the support of a whole of its Fourier transform be Uμsupp{ψμ}=Пi=1^d[Ai, Di]-Пi=1^d（Bi, Ci）, Ai≤Bi≤Ci≤Di. Under the weakest condition that each │ψμ│,... 详细信息

关键词： Orthonormal wavelets Multiresolution analysis Scaling function Compact support

A Formula for the Non-integer Powers of the Laplacian

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Acta Mathematica Sinica,English Series 1999年第1期15卷 21-24页

作者： Zhengxu Hedepartment of mathematics,university of california,San Diego,La Jolla,ca 92093-0112,usa department of mathematics University of California San Diego La Jolla USA

We provide an elementary formula for the non-integer powers of the Laplace operator in the Euclidean *** formulas are helpful in establishing the elliptic nature of some pseudo- differential operators arising from the... 详细信息

关键词： Laplacian Power of Laplacian