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1.
By using concrete isoparametric maps we obtain some new equivariant harmonic maps between spheres and solve equivariant boundary value problems for harmonic maps from unit open ballB m+1 intoS n. Research partially supported by NNSFC, SFECC and ICTP.  相似文献   

2.
Let Aut(D) denote the group of biholomorphic diffeormorphisms from the unit disc D onto itself and O(3) the group of orthogonal transformations of the unit sphere S 2. The existence of multiple solutions to the Dirichlet problem for harmonic maps from D into S 2 is related to the symmetries (if any) of the boundary value γ : ∂DS 2, by invariance of the Dirichlet energy under the action of Aut(D) × O(3). In this paper, we classify the stabilizers in Aut(D) × O(3) of boundary values in H 1/2(S 1, S 2) and . We give two applications to the Dirichlet problem for harmonic maps. This work was partially supported by the CMLA, Ecole Normale Supérieure de Cachan, Cachan, France.  相似文献   

3.
In this paper we consider the Dirichlet problem at infinity of proper harmonic maps from noncompact complex hyperbolic space to a rank one symmetric space N of noncompact type with singular boundary data . Under some conditions on f, we show that the Dirichlet problem at infinity admits a harmonic map which assumes the boundary data f continuously. Received: March 11, 1999 / Accepted April 23, 1999  相似文献   

4.
We consider the heat flow for harmonic maps from Rm to a compact manifold N. When the Lm norm of the gradient of the initial data is small, we prove the existence of a global solution. We prove a similar result for the boundary value problem, when the boundary of the manifold M maps into a point.  相似文献   

5.
Philippe Bonnet 《代数通讯》2013,41(10):3944-3953
Let G be an affine algebraic group over an algebraically closed field k of characteristic zero. In this article, we consider finite G-equivariant morphisms F:X → Y of irreducible affine G-varieties. First we determine under which conditions on Y the induced map F G :X//G → Y//G of quotient varieties is also finite. This result is reformulated in terms of kernels of derivations on k-algebras A ? B such that B is integral over A. Second we construct explicitly two examples of finite G-equivariant maps F. In the first one, F G is quasifinite but not finite. In the second one, F G is not even quasifinite.  相似文献   

6.
Sandier  E.  Soret  M. 《Potential Analysis》2000,13(2):169-184
We prove that the singularities of harmonic maps from a domain D in the plane to S 1 minimizing a renomalized energy tend to go to the boundary when their number becomes large.  相似文献   

7.
We prove existence and uniqueness of weakly harmonic maps from the unit ball in ℝ n (with n≥ 3) to a smooth compact target manifold within the class of maps with small scaled energy for suitable boundary data. Received: 9 June 2000 / Revised version: 17 April 2001  相似文献   

8.
The relationship between harmonic maps from R2 to S2, H2, ST,1, S1,1(–1) and the ± sinh — Laplace, ± sine — Laplace equation is found respectively. Existence theorems of some boundary value problems for the above harmonic maps are obtained. In the cases of H2, S1,1(+1), S1,1(–1) the results are global.Research supported partially by the Institute for Applied Mathematics, Sonderforschungsbereich 72 of the University of Bonn  相似文献   

9.
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   

10.
In this paper we study surfaces in S4 and their twistor Gauss maps. Some necessary and sufficient conditions that the twistor Gauss map is harmonic are given. We find many examples of nonisotropic harmonic maps from a surface to P 3.Supported by the National Natural Science Foundation of China and the Science Foundation of Zhejiang Province.  相似文献   

11.
In this note, we construct some new harmonic maps from ℝ m to ℍ m via symmetric methods. Supportedb y NSF Postdoctoral Research Fellowship, China, and MCSEC.  相似文献   

12.
We give a simple criterion for equivariant harmonic maps into complex projective spaces CP n . As an application of the criterion, we give examples of equivariant harmonic cylinders. We also give examples of non-equivariant harmonic cylinders as perturbations of equivariant harmonic cylinders.  相似文献   

13.
In this paper, by using the technique of integral transformation, we obtain the Plemelj formulas with the Cauchy principal value and the Hadamard principal value of mixed higher order partial derivatives for integral of the Bochner-Martinelli type on a closed smooth manifold ∂D in Cn. From the Plemelj formulas and using the theory of complex partial differential equation, we prove that the problem of higher order boundary value DκΦ+(t) = DκΦ(t) + f(t) is equivalent to a complex linear higher order partial differential equation. Moreover, given a proper condition of the Cauchy boundary value problem, the problem of higher order boundary value has a unique branch complex harmonic solution satisfying Φ(∞) = 0 in Cn\∂D.  相似文献   

14.
We consider the harmonic heat flow for maps u between B3, the unit ball of , and its boundary S2. For a class of possibly singular initial and boundary data we show the existence of a weak solution whose singular set is a fixed discrete set on the vertical axis arbitrarily prescribed. Other examples including isolated singularities moving along a prescribed trajectory are given.Received: 23 October 2002, Accepted: 12 March 2003, Published online: 4 September 2003  相似文献   

15.
Summary We prove several Liouville theorems for harmonic maps between certain classes of Riemannian manifolds. In particular, the results can be applied to harmonic maps from the Euclidean space (R m ,g 0) to a large class of Riemannian manifolds. Our assumptions on the harmonic maps concern the asymptotic behavior of the maps at .Oblatum 28-XII-1990 & 11-II-1991Supported by NSF grant DMS-8610730  相似文献   

16.
LetS 1.1 denote the submanifold of Lorentz spaceR 2.1, which is composed of all pointsl withl 2=1 and letT 1.1=R 1.1/Z×Z. In this paper we study the existence of nontrivial harmonic maps fromT 1.1 toS 1.1 andH 2, and construct a harmonic map for any homotopy class of maps fromT 2 toS 1.1.  相似文献   

17.
Cao  Xiangzhi  Chen  Qun 《中国科学 数学(英文版)》2022,65(11):2371-2378

We consider a kind of generalized harmonic maps, namely, the VT-harmonic maps. We prove an existence theorem for the Dirichlet problem of VT-harmonic maps from compact manifolds with boundary.

  相似文献   

18.
There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S 1-valued function defined on the boundary of a bounded regular domain of R n . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology class induced from the S 1-valued boundary data. The union of this harmonic map and the minimal current is the natural generalization of the harmonic extension. Received December 3, 1998 / final version received May 10, 1999  相似文献   

19.
In this paper we show that a weak heat flow of harmonic maps from a compact Riemannian manifold (possibly with boundary) into a sphere, satisfying the monotonicity inequality and the energy inequality, is regular off a closed set of m-dimensional Hausdorff measure zero.  相似文献   

20.
A representation of the sharp constant in a pointwise estimate for the absolute value of the directional derivative of a harmonic function in a multidimensional ball is obtained under the assumption that the boundary values of the function belong to L p . This representation is specified in the cases of radial and tangential derivatives. It is proved for p = 1 and p = 2 that the maximum of the absolute value of the directional derivative of a harmonic function with a fixed L p -norm of its boundary values is attained at the radial direction. This confirms D. Khavinson’s conjecture for p = 1 and p = 2. Bibliography: 11 titles.  相似文献   

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