共查询到20条相似文献,搜索用时 0 毫秒
1.
De Liang HSU Jia Yu LI 《数学学报(英文版)》2008,24(2):223-226
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. 相似文献
2.
The notion of locally weak monotonicity inequality for weakly harmonic maps is introduced and various results on this class
of maps are obtained. For example, the locally weak monotonicity inequality is nearly equivalent to theε-regularity.
Project supported by the National Natural Science Foundation of China (Grant No. 19571028) and the Guangdong Provincial Natural
Science Foundation of China. 相似文献
3.
周春琴 《高校应用数学学报(A辑)》2002,17(3):323-328
讨论一类映入球面的满足拟单调不等式的弱调和映射的边界正则性。利用函数的延拓技巧以及Hardy空间和BMO空间的对偶性,对这类弱调和映射的边界正则性给出一个简明的证明。 相似文献
4.
L.F. Cheung 《Journal of Mathematical Analysis and Applications》2004,289(1):1-13
We study the effect of the varying y′(0) on the existence and asymptotic behavior of solutions for the initial value problem
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CHU Yuming & LIU Xiangao Department of Mathematics Huzhou Teachers College Huzhou China Institute of Mathematics Fudan University Shanghai China 《中国科学A辑(英文版)》2006,49(5):599-610
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. 相似文献
7.
Atsushi Tachikawa 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1953-1970
We study the energy functional for maps from a Riemannian m-manifold M into a Finsler space N=(Rn,F). Under the restriction 2?m?4, we prove the full Hölder regularity of weakly harmonic maps (i.e., weak solutions of its Euler–Lagrange equation) from M to N in the case that the Finsler structure F(u,X) depends only on vectors X, and a partial Hölder regularity of energy minimizing maps in general cases. 相似文献
8.
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. 相似文献
9.
MO Xiaohuan~ YANG Yunyan~.LMAM School of Mathematical Sciences Peking University Beijing China.Department of Mathematics Renmin University of China Beijing China 《中国科学A辑(英文版)》2005,48(1):115-130
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. 相似文献
10.
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. 相似文献
11.
Xiangao Liu 《中国科学A辑(英文版)》1999,42(11):1184-1192
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. 相似文献
12.
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. 相似文献
13.
Second variation of harmonic maps between Finsler manifolds 总被引:3,自引:0,他引:3
SHEN Yibing & ZHANG YanDepartment of Mathematics Zhejiang University Hangzhou China Correspondence should be addressed to Shen Yibing 《中国科学A辑(英文版)》2004,47(1):39-51
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. 相似文献
14.
Factorization and symplectic uniton numbers for harmonic maps into symplectic groups 总被引:7,自引:0,他引:7
It is proved that any harmonic map ϕ : Ω →Sp(N) from a simply connected domain Ω ⊆R
2⋃ | ∞ | into the symplectic groupSp(N) ⊂U(2N) with finite uniton number can be factorized into a product of a finite number of symplectic unitons. Based on this factorization,
it is proved that the minimal symplectic uniton number of ϕ is not larger thanN, and the minimal uniton number of ϕ is not larger than 2N - 1. The latter has been shown in literature in a quite different way. 相似文献
15.
Min-Chun Hong 《偏微分方程通讯》2013,38(11-12):1967-1985
16.
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. 相似文献
17.
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.
18.
Yuan‐Jen Chiang 《Mathematische Nachrichten》2015,288(17-18):1970-1980
We show that the associated quadratic differentials of exponentially harmonic maps are holomorphic under certain circumstance. We study the sufficient and necessary conditions for axially symmetric maps which are exponentially harmonic. We investigate exponentially harmonic equations for rotationally symmetric maps between rotationally symmetric manifolds of low dimensions. 相似文献
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20.
We obtain theH
1-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical
solutions are attracted to the minimum points of the pinning functions. As a corollary, we construct a self-similar solution
in the evolution of harmonic maps. 相似文献