| 1. | The variational calculation of potential p - harmonic maps
调和映射的变分计算 |
| 2. | On harmonic maps into a real form of unitary group u
到酉群实形式的调和映射 |
| 3. | Teichm ller mappings and harmonic maps
映射与调和映射 |
| 4. | In chapter two , we propose a mesh fusion algorithm base on local harmonic mapping . compared with the global harmonic mapping method , this approach has the following advantages
在第二章中，我们提出了基于局部调和映射的网格融合方法。 |
| 5. | Image and vision computing , 1999 , 17 : 201 - 212 . 9 tang b , sapiro g , caselles v . diffusion of general data on non - flat manifolds via harmonic maps theory : the direction diffusion case
通过对线性四元数扩散方程的近似解进行研究，证明了当方程的参数在一定范围内可以具有对于颜色图像导数的归整化。 |
| 6. | In 4 we obtain an explicit formula to calculate ord ( ) which is suitable for any harmonic map of m into g ( m , n ) . moreover , the formula depends on ( p only and is independent of 0 )
在妇中我们给出了ord (司的一个显式计算公式，它适用于任意汀到侧二，哟的调和映照，而且计算公式只与甲有关而与笋。 |
| 7. | For a given harmonic map . it is natural to ask that when the harmonic map is " - irreducible or " - irreducible , and when is isotropic ? if is non - isotropic , how to calaulate its isotropy order ? these are all the elementary topics for harmonic maps
如果它是非迷向的，又如何确定它的迷向阶?这些都是关于调和映照的基本问题。料的主要目的就是要解决这些问题。 |
| 8. | The second part consist of chapter four . in chapter one , we study the energy density of harmonic map from finsler manifold and generalize classical result in [ se ] . in chapter two , we obtain lower estimates for the first eigenvalue of the laplace operator on a compact finsler manifold , and it generalize lichnerowicz - obata theorem [ li ] [ ob ] . in chapter three , we derive the first and second variation formula for harmonic maps between finsler manifolds . as an application , some nonexistence theorems of nonconstant stable harmonic maps from a finsler manifold to a riemannian manifold are given
第一章讨论finsler流形到黎曼流形调和映射的能量密度的间隙性，推广了[ se ]中的结果。第二章对紧致finsler流形上laplace算子的第一特征值的下界作了估计，推广了黎曼流形上的lichnerowicz - obata定理[ li ] [ ob ] 。 |
| 9. | This paper is to study harmonic maps into symplectic groups and local isometric immersions into space forms by means of the soliton theory . by realizing an action of the rational loop group on the spaces of corrsponding solutions , we get the backlund transformation and the darboux transformation , and thereby we give the explicit construction for harmonic maps into symplectic groups and local isometric immersions into space forms via purely algebraic algorithm
主要用孤立子理论研究到辛群的调和映射和到空间形式的局部等距浸入，通过有理loop群在其解空间上的dressing作用，给出b icklund变换和darboux变换的显式表示，从而获得到辛群及其对称空间的调和映射和到空间形式的局部等距浸入的纯代数构造方法。 |
| 10. | Harmonic maps between riemannian manifolds are very important in both differential geometry and mathematical physics . riemannian manifold and finsler manifold are metric measure space , so we can study harmonic map between finsler manifolds by the theory of harmonic map on general metric measure space , it will be hard to study harmonic map between finsler manifolds by tensor analysis and it will be no distinctions between the theory of harmonic map on finsler manifold and that of metric measure space . harmonic map between riemannian manifold also can be viewed as the harmonic map between tangent bundles of source manifold and target manifold
黎曼流形间的调和映射是微分几何和数学物理的重要内容。黎曼流形和finsler流形都是度量空间，自然可利用一般度量空间调和映射的理论讨论finsler流形间的调和映射。但由于控制finsler流形性质的各种张量一般情况下很难应用到一般度量空间调和映射的理论中，使得这样的讨论大都是形式上的，并与一般度量空间调和映射的理论区别不大。 |
