共查询到20条相似文献,搜索用时 343 毫秒
1.
We define and develop an interior partial regularity theory for intrinsic energy minimising fractional harmonic maps from Euclidean space into smooth compact Riemannian manifolds for fractional powers strictly between zero and one. Intrinsic fractional harmonic maps are critical points of an energy whose first variation is a Dirichlet to Neumann map for the harmonic map problem on a half-space with a Riemannian metric which can degenerate/become singular along the boundary, depending on the fractional power. Similarly to the approach used to prove regularity for stationary intrinsic semi-harmonic maps, we take advantage of the connection between fractional harmonic maps and free boundary problems for harmonic maps in order to develop a partial regularity theory for the fractional harmonic maps we consider. In particular, we prove partial regularity for locally minimising harmonic maps with (partially) free boundary data on half-spaces with the aforementioned metrics up to the boundary; fractional harmonic maps then inherit this regularity. As a by-product of our methods we shed some new light on the monotonicity of the average energy of solutions of the degenerate linear elliptic equation related to fractional harmonic functions. 相似文献
2.
Bayram Sahin 《Proceedings Mathematical Sciences》2008,118(4):573-581
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. 相似文献
3.
本文给出一类带由边界的调和映射的Liouville型定理,这种类型的定理在微分几何的一些问题中有十分重要的应用.我们通过对调和映射的能量选取特殊的变分族,得到任意从半空间的简单流形到一黎曼流形的带自由边界的调和映射在如果满足适当的条件(见定理)必为常值映射的结果. 相似文献
4.
Bernd Ammann Nicolas Ginoux 《Calculus of Variations and Partial Differential Equations》2013,47(3-4):739-762
We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the source and target manifolds is a harmonic map. 相似文献
5.
Nonlinear versions of Bismut type formulas for the differential of a harmonic map between Riemannian manifolds are used to establish a priori estimates for harmonic maps. A variety of Liouville type theorems is shown to follow as corollaries from such estimates by exhausting the domain through an increasing sequence of geodesic balls. This probabilistic method is well suited for proving sharp estimates under various curvature conditions. We discuss Liouville theorems for harmonic maps under the following conditions: small image, sublinear growth, non-positively curved targets, generalized bounded dilatation, Liouville manifolds as domains, certain asymptotic behaviour. 相似文献
6.
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.
7.
8.
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
9.
Yuanlong Xin 《数学学报(英文版)》1999,15(2):277-292
Some Liouville type theorems for harmonic maps from Kähler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (exceptR IV(2)) to any Riemannian manifold with finite energy has to be constant. 相似文献
10.
Wei-Yue Ding 《manuscripta mathematica》1994,85(1):283-297
By introducing the “relative energy”, we develop a new method for finding harmonic maps from noncompact complete Riemannian manifolds with prescribed asympototic behaviour at infinity. This method is an extension of the well known direct method of energy-minimization for compact domains. As an application of our method, we show that the Dirichlet problem at infinity with Hölder continuous boundary data for harmonic maps from a Cartan-Hadarmard manifold with bounded negative curvature into a compact manifold, has a locally minimizing solution which is smooth near infinity. 相似文献
11.
We establish a Weitzenböck formula for harmonic morphismsbetween Riemannian manifolds and show that under suitable curvatureconditions, such a map is totally geodesic. As an applicationof the Weitzenböck formula we obtain some non-existenceresults of a global nature for harmonic morphisms and totallygeodesic horizontally conformal maps between compact Riemannianmanifolds. In particular, it is shown that the only harmonicmorphisms from a Riemannian symmetric space of compact typeto a compact Riemann surface of genus at least 1 are the constantmaps. 相似文献
12.
Lars Schaefer 《Geometriae Dedicata》2007,128(1):107-112
First, we generalize a rigidity result for harmonic maps of Gordon (Gordon (1972) Proc AM Math Soc 33: 433–437) to generalized pluriharmonic maps. We give the construction of generalized pluriharmonic maps from metric tt *-bundles over nearly Kähler manifolds. An application of the last two results is that any metric tt *-bundle over a compact nearly Kähler manifold is trivial (Theorem A). This result we apply to special Kähler manifolds to show that any compact special Kähler manifold is trivial. This is Lu’s theorem (Lu (1999) Math Ann 313: 711–713) for the case of compact special Kähler manifolds. Further we introduce harmonic bundles over nearly Kähler manifolds and study the implications of Theorem A for tt *-bundles coming from harmonic bundles over nearly Kähler manifolds. 相似文献
13.
J. C. Wood 《Journal of Mathematical Sciences》1999,94(2):1263-1269
A harmonic morphism is a map between Riemannian manifolds which preserves Laplace's equation. We compare the properties of
harmonic morphisms with those of the better known harmonic maps, seeing that they behave in some ways “dual” to the latter.
In particular, we give representation theorems for harmonic morphisms in low dimensions which suggest that the equations might
be soluble in some cases by integrable-system techniques in a similar way to that used in harmonic map theory. Bibliography:
38 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 190–200. 相似文献
14.
The heat flow for Dirac-harmonic maps on Riemannian spin manifolds is a modification of the classical heat flow for harmonic maps by coupling it to a spinor. It was introduced by Chen, Jost, Sun, and Zhu as a tool to get a general existence program for Dirac-harmonic maps. For source manifolds with boundary they obtained short time existence, and the existence of a global weak solution was established by Jost, Liu, and Zhu. We prove short time existence of the heat flow for Dirac-harmonic maps on closed manifolds. 相似文献
15.
Joseph F. Grotowski 《Journal of Geometric Analysis》1993,3(3):279-292
We examine the existence problem for harmonic maps between the three-dimensional ball and the two-sphere. We utilize results on the classification of harmonic maps into hemispheres and a result on the regularity of the weak limit of energy minimizers over the class of axially symmetric maps to establish the existence of asmooth harmonic extension for boundary data suitably “concentrated” away from the axis of symmetry. In addition, we establish convergence results for the harmonic map heat flow problem for suitably “concentrated” axially symmetric initial and boundary data. 相似文献
16.
本文建立了从曲面到复Grassmamn流形调和映照的广义Frenet公式。作为应用,我们得到了调和映照为强共形的一个等价条件。我们也讨论了等距调和映照的曲率pinching性质。从而改进了有关伪全纯曲线的相应结果。 相似文献
17.
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.
Seddik Ouakkas 《Differential Geometry and its Applications》2008,26(5):495-502
We consider harmonic semi-conformal maps between two Riemannian manifolds. By deforming conformally the codomain metric, we construct new examples of non-harmonic biharmonic maps. 相似文献
19.
Let M
m
and N be two compact Riemannian manifolds without boundary. We consider the L
2 gradient flow for the energy
. If
and N has nonpositive sectional curvature we show that the biharmonic map heat flow exists for all time, and that the solution subconverges to a smooth harmonic map as time goes to infinity. This reproves the celebrated theorem of Eells and Sampson [6] on the existence of harmonic maps in homotopy classes for domain manifolds with dimension less than or equal to 4.Received: 27 March 2003, Accepted: 5 April 2004, Published online: 16 July 2004Mathematics Subject Classification (2000):
58E20, 58J35 相似文献
20.
Youde Wang 《偏微分方程(英文版)》1999,12(3):262-280
ln this paper we prove some general existence theorems of harmonic maps from complete noncompact manifolds with tho positive lower bounds of spectrum into convex balls. We solve the Dirichlet problem in classical domains and some special complete noncompact manifolds for harmonic maps into convex balls. We also study the existence of harmonic maps from some special complete noncompact manifolds into complete manifolds with nonpositive sectional curvature which are not simply connected. 相似文献