Stable Stationary Harmonic Maps to Spheres

For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S^k. We show that the singular set of stable-stationary harmonic maps from B5 to 83 is the union of finitely many isolated singular points and finitely many HSlder continuous curves. We also discuss the minimization problem among continuous maps from B^n to S^2.     

P-调和映射流的存在性与不唯一性

构造了ｐ 调和发展方程的初边值问题的一个整体弱解；证明了当初值ｕ０（ｘ）是弱ｐ 调和映射但不是弱ｐ 驻调和映射时问题弱解的不唯一性．     

Non-existence for Harmonic Maps on Complete Noncompact Manifolds

In this paper, we prove a nonexistence theorem on harmonic maps. This generalizes the well-known Liouville-type theorem on harmonic maps due to S.Y. Cheng and H.I Choi.     

Hermitian调和映照的Schwarz引理

由Jost和Yau引进的Hermitian调和映照是Riemannian流形上通常的调和映照在Hermitian流形上的一种自然的类比.本文证明了复分析中经典的Schwarz引理对一大类Hermitian调和映照仍然成立.作为推论,我们得到了半共形Hermitian调和映照的Liouville性质.     

An approach to the regularity for stable-stationary harmonic maps

In this paper we investigate the regularity of stable-stationary harmonic maps. By assuming that the target manifolds do not carry any stable harmonic , we obtain some compactness results and regularity theorems. In particular, we prove that the Hausdorff dimension of the singular set of these maps cannot exceed , and the dimension estimate is optimal.

     

Harmonic Maps Over Rings

For the torsion-free modules over noncommutative principal ideal domains von Staudt's theorem is proved. Moreover, more general (nonbijective) harmonic maps with the classical definition of harmonic quadruple is calculated.     

稳定调和映照的不存在性

讨论了从Finsler流形到Riemannian流形的稳定调和映照的不存在性,得到了一个拼挤定理.     

Standard realizations of crystal lattices via harmonic maps

An Eells-Sampson type theorem for harmonic maps from a finite weighted graph is employed to characterize the equilibrium configurations of crystals. It is thus observed that the mimimum principle frames symmetry of crystals.

     

Stationary harmonic maps into complete Riemannian manifold

The stationary for harmonic maps is considered from a Riemannian manifoldM into a complete Riemannian manifoldN without boundary, and it is proved that its singular set is contained inQ ¹ 2MQ ³ Project supported partially by the Development Foundation Science of Shanghai, China.     

The existence of harmonic maps from Finsler manifolds of Riemannian manifolds

In this paper,we consider the existence of harmonic maps from a Finsler manifold and study the characterisation of harmonic maps,in the spirit of Ishihara.Using heat quation method we show that any map from a compact Finsler manifold M to a compact Riemannian manifold with non-positive sectional curvature can be deformed into a harmonic map which has minimum energy in its homotopy class.     

X-调和映射的稳定性

在一般调和映射基础上定义了X-调和映射和次椭圆调和映射，得到了X-调和映射的稳定性定理，它是Leung一般调和映射及其稳定性定理的推广．     

FATOU PROPERTY ON HARMONIC MAPS FROM COMPLETE MANIFOLDS WITH NONNEGATIVE CURVATURE AT INFINITY INTO CONVEX BALLS

ＦＡＴＯＵＰＲＯＰＥＲＴＹＯＮＨＡＲＭＯＮＩＣＭＡＰＳＦＲＯＭＣＯＭＰＬＥＴＥＭＡＮＩＦＯＬＤＳＷＩＴＨＮＯＮＮＥＧＡＴＩＶＥＣＵＲＶＡＴＵＲＥＡＴＩＮＦＩＮＩＴＹＩＮＴＯＣＯＮＶＥＸＢＡＬＬＳ￥ＹＡＮＧＹＩＨＵＡｂｓｔｒａｃｔ：Ｔｈｅａｕｔｈｏｒｃ...     

G2,n中的可兼共形调和曲面

本文通过建立复Ｇｒａｓｓｍａｎｎ流形Ｇ２，ｎ中调和曲面的Ｇａｕｓｓ丛的基本公式，在适当的拓扑条件下给出了Ｇ２，ｎ中可兼共形调和曲面的构造定理．推广和改进了Ｂｕｒｓｔａｌｌ和Ｗｏｏｄ的低亏格曲面的结果．     

The existence of harmonic maps from Finsler manifolds to Riemannian manifolds

In this paper,we consider the existence of harmonic maps from a Finsler man-ifold and study the characterisation of harmonic maps,in the spirit of lshihara.Using heatequation method we show that any map from a compact Finsler manifold M to a com-pact Riemannian manifold with non-positive sectional curvature can be deformed into aharmonic map which has minimum energy in its homotopy class.     

Harmonic Riemannian maps on locally conformal Kaehler manifolds

We study harmonic Riemannian maps on locally conformal Kaehler manifolds (lcK manifolds). We show that if a Riemannian holomorphic map between lcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the lcK manifold is Kaehler. Then we find similar results for Riemannian maps between lcK manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.     

Vanishing theorems for ach Kähler manifolds and harmonic maps

We discuss a class of complete Kähler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L ² cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincaré inequality case and establish a vanishing theorem provided that the weighted function ρ is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincaré inequality.     

A Bridge Principle for Harmonic Maps

We prove a bridge principle for harmonic maps between generalmanifolds.     

靶流形为球面子流形的调和映射的量子化现象(英文)

本文研究了调和映射和极小子流形的量子化性质.通过运用谱分解方法,获得了靶流形为球面子流形的调和映射的量子化性质,然后将其应用到球面的极小子流形的高斯映射,得到了极小子流形的第二基本形式的量子化性子.     

稳定拟调和映照的不存在性

本文讨论了稳定拟调和映照的不存在性，得到了一个拼挤定理。     

A finiteness theorem of harmonic maps from compact lie groups toO HS(H)

In this article we study the behavior of harmonic maps from compact connected Lie groups with bi-invariant metrics into a Hilbert orthogonal group. In particular, we will demonstrate that any such harmonic map always has image contained within someO(n),n<∞. Since homomorphisms are a special subset of the harmonic maps we get as a corollary an extension of the Peter-Weyl theorem, namely, that every representation of a connected compact Lie group is finite dimensional. This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.