• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal d'analyse mathematique >Classifying Complex Geodesics for the Caratheodory Metric on Low-Dimensional Teichmuller Spaces
【24h】

Classifying Complex Geodesics for the Caratheodory Metric on Low-Dimensional Teichmuller Spaces

机译：对低维Teichmuller空间上的加工园度量进行分类复杂测地测量

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

It was recently shown that the Caratheodory and Teichmuller metrics on the Teichmuller space of a closed surface do not coincide. On the other hand, Kra earlier showed that the metrics coincide when restricted to a Teichmuller disk generated by a differential with no odd-order zeros. Our aim is to classify Teichmuller disks on which the two metrics agree, and we conjecture that the Caratheodory and Teichmuller metrics agree on a Teichmuller disk if and only if the Teichmuller disk is generated by a differential with no odd-order zeros. Using dynamical results of Minsky, Smillie, and Weiss, we show that it suffices to consider disks generated by Jenkins-Strebel differentials. We then prove a complex-analytic criterion characterizing Jenkins-Strebel differentials which generate disks on which the metrics coincide. Finally, we use this criterion to prove the conjecture for the Teichmuller spaces of the five-times punctured sphere and the twice-punctured torus. We also extend the result that the Caratheodory and Teichmuller metrics are different to the case of compact surfaces with punctures.
机译：最近据表明，封闭表面的Teichmuller空间上的加工统计和Teichmuller指标不一致。另一方面，KRA之前，指标在仅限于没有奇数零的差分产生的TeichMuller磁盘时重合。我们的目标是对这两个指标同意的Teichmuller磁盘同意，并且我们猜测Caratheodory和Teichmuller指标在TeichMuller磁盘上同意，如果只有TeichMuller磁盘由没有奇数零点的差分生成。使用Minsky，Smillie和Weiss的动态结果，我们表明它足以考虑Jenkins-Streebel差异产生的磁盘。然后，我们证明了一个复杂的分析标准，其特征在于jenkins-strebel差异，它生成指标符合指标的磁盘。最后，我们使用该标准来证明五次刺破球体的Teichmuller空间和两次刺破的圆环的猜想。我们还延长了加工统计和Teichmuller指标与具有穿孔的紧凑型表面的情况不同。

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