共查询到20条相似文献,搜索用时 15 毫秒
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Michael Struwe 《manuscripta mathematica》1998,96(4):463-486
Harmonic maps from B
1 (0, ℝ3) to a smooth compact target manifold N with uniformly small scaled energy (see assumption (2) below) are shown to be unique for their boundary values.
Received: 12 May 1997 相似文献
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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
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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
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Wang Youning 《数学学报(英文版)》1990,6(1):57-64
In this paper, we establish a sharp inequality of the gradient of energy density. We use it in studying stability of domain and pinching of energy. And we get the sharp conclusion respectly. In addition, we connect the existence of non-constant totally geodesic maps with the construction of manifolds on topology and geometry. 相似文献
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We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map. 相似文献
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Volker Branding 《Archiv der Mathematik》2017,108(2):151-157
We call the \({\delta}\)-vector of an integral convex polytope of dimension d flat if the \({\delta}\)-vector is of the form \({(1,0,\ldots,0,a,\ldots,a,0,\ldots,0)}\), where \({a \geq 1}\). In this paper, we give the complete characterization of possible flat \({\delta}\)-vectors. Moreover, for an integral convex polytope \({\mathcal{P}\subset \mathbb{R}^N}\) of dimension d, we let \({i(\mathcal{P},n)=|n\mathcal{P}\cap \mathbb{Z}^N|}\) and \({i^*(\mathcal{P},n)=|n(\mathcal{P} {\setminus}\partial \mathcal{P})\cap \mathbb{Z}^N|}\). By this characterization, we show that for any \({d \geq 1}\) and for any \({k,\ell \geq 0}\) with \({k+\ell \leq d-1}\), there exist integral convex polytopes \({\mathcal{P}}\) and \({\mathcal{Q}}\) of dimension d such that (i) For \({t=1,\ldots,k}\), we have \({i(\mathcal{P},t)=i(\mathcal{Q},t),}\) (ii) For \({t=1,\ldots,\ell}\), we have \({i^*(\mathcal{P},t)=i^*(\mathcal{Q},t)}\), and (iii) \({i(\mathcal{P},k+1) \neq i(\mathcal{Q},k+1)}\) and \({i^*(\mathcal{P},\ell+1)\neq i^*(\mathcal{Q},\ell+1)}\). 相似文献
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If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism
from A to a twisted homogeneous coordinate ring , which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies
on some results concerning the growth of graded rings which are of independent interest.
D. Rogalski was partially supported by NSF grant DMS-0202479.
J. J. Zhang was partially supported by NSF grant DMS-0245420 and Leverhulme Research Interchange Grant F/00158/X (UK). 相似文献
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Ming Li 《Calculus of Variations and Partial Differential Equations》1995,3(4):513-529
In this paper, we study energy minimizing harmonic maps into a complete Riemannian manifold. We prove that the singular set of such a map has Hausdorff dimension at mostn–2, wheren is the dimension of the domain. We will also give an example of an energy minimizing map from surface to surface that has a singular point. Thus then–2 dimension estimate is optimal, in contrast to then–3 dimension estimate of Schoen-Uhlenbeck [SU] for compact targets. 相似文献
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Alexandre Freire Stefan Müller Michael Struwe 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》1998,15(6):725
We show that a weak limit of a sequence of wave maps in (1 + 2) dimensions with uniformly bounded energy is again a wave map. Essential ingredients in the proof are Hodge structures related to harmonic maps,
1 estimates for Jacobians,
1-BMO duality, a “monotonicity” formula in the hyperbolic context and the concentration compactness method. Application of similar ideas in the elliptic context yields a drastically shortened proof of recent results by Bethuel on Palais-Smale sequences for the harmonic map functional on two dimensional domains and on limits of almost H-surfaces. 相似文献
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Subelliptic harmonic maps 总被引:7,自引:0,他引:7
Jü rgen Jost Chao-Jiang Xu 《Transactions of the American Mathematical Society》1998,350(11):4633-4649
We study a nonlinear harmonic map type system of subelliptic PDE. In particular, we solve the Dirichlet problem with image contained in a convex ball.
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We present an elementary argument of the regularity of weak harmonic maps of a surface into the spheres, as well as the partial regularity of stationary harmonic maps of a higher‐dimensional domain into the spheres. The argument does not make use of the structure of Hardy spaces. © 1999 John Wiley & Sons, Inc. 相似文献
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