Analytic and harmonic maps into a topological space

The relationship between the harmonicity and analyticity of a continuous map from the open unit disc to the underlying space of a real algebra is investigated.     

曲面到U（N）中有限的调和映射

本文证明了如果ｓ是从曲面Ω到Ｕ（Ｎ）中有限的调和映射，则Ａｚ，Ａｚ－是幂零的，并给出其逆不成立的反例。     

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.     

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.

     

On Factorization of Harmonic Maps of Surfaces into U(N) and Action of Groups

§ 0 .Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＣｂｅｔｈｅｃｏｍｐｌｅｘｐｌａｎｅ ,ΩａｓｉｍｐｌｅｃｏｎｎｅｃｔｅｄｄｏｍａｉｎｉｎＣ∪ {∞ },ａｎｄＵ(Ｎ)ｔｈｅｒｅａｌｆｏｒｍｏｆｔｈｅｃｏｍｐｌｅｘ ｇｒｏｕｐＧＬ (Ｎ ,Ｃ) .Ｉｆｓ :Ω→Ｕ (Ｎ )ｉｓａｈａｒｍｏｎｉｃｍａｐ ,Ｕｈｌｅｎｂｅｃｋ[1] ｄｅｆｉｎｅｄｔｈｅｅｘｔｅｎｄｅｄｓｏｌｕｔｉｏｎＥλｏｆｓ,λ∈Ｃ \{0 },ｗｈｉｃｈｍａｙｂｅｅｘｐａｎｄｅｄｉｎｔｏａＬａｕｒｅｎｔｓｅｒｉｅｓ ∑+∞α=-∞λαＴα,ｓ=ＱＥ-1,ｗｈｅｒｅＱ∈Ｕ(Ｎ)ｉｓａｃ…     

On the Regularity for Stationary Harmonic Maps

We prove a compactness theorem for k-indexed stationary harmonic maps, and show a regularity theorem for this kind of maps which says that the singular set of a k-indexed stationary harmonic map is of Hausdorff dimension at most m-3.     

Constructive factorizations of imitons via singular Darboux transformations

Some new factorizations of unitons into Lie groups are established via singular Darboux transformations. The factorization processes for Grassmannian unitons are also considered. Furthermore, a purely algebraic method for constructing Grassmannian unitons is presented.     

Regularity of harmonic maps with the potential

The aim of this work is to prove the partial regularity of the harmonic maps with potential. The main difficulty caused by the potential is how to find the equation satisfied by the scaling function. Under the assumption on the potential we can obtain the equation, however, for a general potential, even if it is smooth, the partial regularity is still open.     

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.     

Bijective maps on standard Borel subgroup of symplectic group preserving commutators

Let F be a field, and let \mathbbG\mathbb{G} be the standard Borel subgroup of the symplectic group Sp(2m, F). In this paper, we characterize the bijective maps ϕ: \mathbbG\mathbb{G} → \mathbbG\mathbb{G} satisfying ϕ[x, y] = [ϕ(x), ϕ(y)].     

Regular Cayley maps for finite abelian groups

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving automorphism group G acts regularly on the directed edge set and has a subgroup isomorphic to A that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical form for A. The case when A is normal in G involves the relationship between the rank of A and the exponent of the automorphism group of A, and the general case uses Ito's theorem to analyze the factorization G = AY, where Y is the (cyclic) stabilizer of a vertex. Supported in part by the N.Z. Marsden Fund (grant no. UOA0124).     

Cross characteristic representations of even characteristic symplectic groups

We classify the small irreducible representations of with even in odd characteristic. This improves even the known results for complex representations. The smallest representation for this group is much larger than in the case when is odd. This makes the problem much more difficult.

     

Second variation of harmonic maps between Finsler manifolds

The first and second variation formulas of the energy functional for a nonde-generate map between Finsler manifolds is derived. As an application, some nonexistence theorems of nonconstant stable harmonic maps from a Finsler manifold to a Riemannian manifold are given.     

Heat flow of harmonic maps from noncompact manifolds

The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.     

On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies

We study bifurcations of two-dimensional symplectic maps with quadratic homoclinic tangencies and prove results on the existence of cascade of elliptic periodic points for one and two parameter general unfoldings.      

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.     

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.