• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Chinese science bulletin >On the boundary value problem for harmonic maps of the Poineare disc
【24h】

On the boundary value problem for harmonic maps of the Poineare disc

机译：关于Poineare盘调和映射的边值问题。

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. It is shown that for any given quasisymmetric homeomorphism h: S~1 -> S~1 EUR T~*. , there is a unique quasiconforrnal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B~*. IT is well known that there are some deep connections between the harmonic maps of compact surfaces with the Poincare metric and the theory of the Teichmuller space of compact Riemann surfaces (see Eells and Sampson , Hartman, Schoen and Yau, and Wolf). Let S~0 be a fixed Riemann surface of genus g > 1. It is shown that for each holomorphic quadratic differential PHI on S_0 there is a unique point [f: S_0 -> S] of the Teiehmuller space T( S_0) such that the Hopf differential of the harmonic map of S_0 to S in the homotopy class of f is PHI. Moreover, such a correspondenceof the space of quadratic differentials on S_0 to the Teichmuller space T(S_0) is a diffeomorphism. Based on these results, some properties of the Teichmuller space of a compact Riemann surface can be established without the theory of quasiconformal mappings. To generalize these results from the case of compact surfaces to the case of non-compact surfaces, Schoen, Wan, Li and Tam, and Tarn and Wan investigated the harmonic maps of the Poincare disc D and established some analogic connection between theuniversal Teichmuller space and harmonic maps of the Poincare disc D.
机译：讨论了庞加莱圆盘调和图的边值问题。重点在于问题中给定边界值的不平滑性。结果表明，对于任何给定的拟对称同胚h：S〜1-> S〜1 EUR T〜*。 ，相对于庞加莱度量，存在一个唯一的D的准圆锥形谐波图，其边界对应的是h，并且该谐波图的Hopf微分属于B〜*。众所周知，在具有Poincare度量的紧致曲面的调和图与紧致黎曼曲面的Teichmuller空间理论之间存在着很深的联系（请参阅Eells和Sampson，Hartman，Schoen和Yau和Wolf）。令S〜0是g> 1的固定Riemann曲面。它表明，对于S_0上的每个全纯二次微分PHI，Teiehmuller空间T（S_0）有一个唯一点[f：S_0-> S]，使得f的同伦类中S_0到S的谐波图的Hopf微分是PHI。此外，S_0上的二次微分空间与Teichmuller空间T（S_0）的这种对应关系是微分同构。基于这些结果，无需拟保形映射的理论就可以建立致密Riemann曲面的Teichmuller空间的某些性质。为了将这些结果从紧实表面的情况推广到非紧实表面的情况，Schoen，Wan，Li和Tam以及Tarn和Wan研究了Poincare圆盘D的调和图，并建立了通​​用Teichmuller空间与Poincare光盘D的谐波图

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号