共查询到20条相似文献,搜索用时 10 毫秒
1.
C. Greco 《Proceedings of the American Mathematical Society》2001,129(4):1199-1206
We consider the problem of minimizing the energy of the maps from the annulus to such that is equal to for , and to , for , where is a fixed angle.
We prove that the minimum is attained at a unique harmonic map which is a planar map if , while it is not planar in the case \pi^2$">.
Moreover, we show that tends to as , where minimizes the energy of the maps from to , with the boundary condition , .
2.
Yang Xuefeng 《数学学报(英文版)》1993,9(4):401-405
In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere inℝ
3 with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary
value isS
1-equivariant and nonconstant.
This research partially supported by the NNSF, P.R. China. 相似文献
3.
Here we obtain various results on the class of axially symmetric harmonic maps from B 3 to S 2. We find some new classes of non-minimizing harmonic maps exhibiting unusual singular behavior. Optimal partial regularity estimates are obtained for mappings which minimize, among axially symmetric maps, various relaxed energies which have been studied in [4]and [11]. 相似文献
4.
Peter Quast 《Differential Geometry and its Applications》2009,27(1):1-6
Given a twistor space over a Hermitian symmetric space of compact type we construct a map onto a twistor space over another inner symmetric space of compact type. This map is holomorphic and preserves the superhorizontal distributions. We describe an application to harmonic maps. 相似文献
5.
An asymptotic ray method is developed for studying propagation of high-frequency harmonic elastic waves from a smooth, convex, axially symmetric cavity. The dynamic stresses near a prolate spheroidal cavity, to whose surface is applied a normal, angle-independent load, are investigated as a specific numerical example. It is shown that account of three terms of the ray series makes it possible to find quite accurate solutions even when the wave length is comparable with the cavity sizes.Translated from Teorr eticheskaya i Prikladnaya Mekhanika, No. 18, pp. 87–95, 1987. 相似文献
6.
Joseph F. Grotowski 《manuscripta mathematica》1991,73(1):207-228
We examine the harmonic map heat flow problem for maps between the three-dimensional ball and the two-sphere. We give blow-up
results for certain initial data. We establish convergence results for suitable axially symmetric initial data, and discuss
generalizations to higher dimensions. 相似文献
7.
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
8.
Karsten Große-Brauckmann 《manuscripta mathematica》1992,77(1):89-95
We derive monotonicity formulas for stationary harmonic maps. The proofs are given in coordinates. 相似文献
9.
Jiayu Li 《Mathematische Zeitschrift》1994,217(1):487-495
10.
11.
James A. McCoy Fatemah Y. Y. Mofarreh Graham H. Williams 《Annali di Matematica Pura ed Applicata》2014,193(5):1443-1455
Inspired by earlier results on the quasilinear mean curvature flow, and recent investigations of fully nonlinear curvature flow of closed hypersurfaces which are not convex, we consider contraction of axially symmetric hypersurfaces by convex, degree-one homogeneous fully nonlinear functions of curvature. With a natural class of Neumann boundary conditions, we show that evolving hypersurfaces exist for a finite maximal time. The maximal time is characterised by a curvature singularity at either boundary. Some results continue to hold in the cases of mixed Neumann–Dirichlet boundary conditions and more general curvature-dependent speeds. 相似文献
12.
13.
Jingyi Chen 《Proceedings of the American Mathematical Society》1996,124(9):2853-2862
We study the existence and uniqueness problems for Hermitian harmonic maps from Hermitian manifolds with boundary to Riemannian manifolds of nonpositive sectional curvature and with convex boundary. The complex analyticity of such maps and the related rigidity problems are also investigated.
14.
15.
Christoph Scheven 《Calculus of Variations and Partial Differential Equations》2006,25(4):409-429
Let
and
be Riemannian manifolds,
compact without boundary. We develop a definition of a variationally harmonic map
with respect to a general boundary condition of the kind u(x)∊Γ(x) for a.e.
, where
are given submanifolds depending smoothly on x. The given definition of variationally harmonic maps is slightly more restrictive, but also more natural than the usual definition
of stationary harmonic maps. After deducing an energy monotonicity formula, it is possible to derive a regularity theory for
variationally harmonic maps with general boundary data. The results include full boundary regularity in the Dirichlet boundary
case Γ(x) = {g(x)} for
if
does not carry a nonconstant harmonic 2-sphere. 相似文献
16.
Christoph Scheven 《Mathematische Zeitschrift》2006,253(1):135-157
Let and be smooth Riemannian manifolds, of the dimension n≥2 with nonempty boundary, and compact without boundary. We consider stationary harmonic maps u ∈ H1(, ) with a free boundary condition of the type u(∂) ⊂ Γ, given a submanifold Γ⊂. We prove partial boundary regularity, namely (sing(u))=0, a result that was until now only known in the interior of the domain (see [B]). The key of the proof is a new lemma
that allows an extension of u by a reflection construction. Once the partial regularity theorem is known, it is possible to reduce the dimension of the
singular set further under additional assumptions on the target manifold and the submanifold Γ. 相似文献
17.
18.
We prove global regularity for the solution to the Cauchy problem with regular data for an equivariant harmonic map from the 2 + 1-dimensional Minkowski space into a two-dimensional, rotationally symmetric, and geodesically convex Riemannian manifold. 相似文献
19.
Atsushi Tachikawa 《manuscripta mathematica》1985,53(3):235-254
This paper deals with the existence problem for rotationally symmetric harmonic maps from an Euclidean unit ball B n or n into a warped product manifold Nf=[0, r0)xfSn–1. 相似文献
20.
We consider partial regularity for energy minimizing maps satisfying a partially free boundary condition. This condition takes
the form of the requirement that a relatively open subset of the boundary of the domain manifold be mapped into a closed submanifold
with non-empty boundary, contained in the target manifold. We obtain an optimal estimate on the Hausdorff dimension of the
singular set of such a map. Our result can be interpreted as regularity result for a vector-valued Signorini, or thin-obstacle,
problem. 相似文献