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<p>Gupta showed that for a grafting ray, there is a Teichmüller ray which is asymptotic to the grafting ray. We consider the decrease speed of the Teichmüller distance between the grafting and Teichmüller rays. Based on Gupta’s method, we give a more explicit estimate of the distance and show that given a grafting ray determined by an arational measured lamination, there exists a Teichmüller ray such that the Teichmüller distance between them decreases as a negative exponential function.</p>

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The exponential asymptotic behavior of grafting and Teichmüller rays

  • 期刊论文

  • 发表日期：

    2025年4月10日

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  • Zhiyang Lyu,
  • Hideki Miyachi,
  • Yi Qi

摘要

Gupta showed that for a grafting ray, there is a Teichmüller ray which is asymptotic to the grafting ray. We consider the decrease speed of the Teichmüller distance between the grafting and Teichmüller rays. Based on Gupta’s method, we give a more explicit estimate of the distance and show that given a grafting ray determined by an arational measured lamination, there exists a Teichmüller ray such that the Teichmüller distance between them decreases as a negative exponential function.