Thurston边界中的无穷远星
Stars at infinity in the Thurston boundary
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中文总结 AI 辅助
该研究针对Thurston和Teichmüller度量下Teichmüller空间的Thurston边界，明确了射影测度叶状结构的星及基于星的性质，扩展了Liu-Shi的定理并否定了Karlsson的猜想。
中文摘要 AI 辅助
我们研究Thurston度量和Teichmüller度量下Teichmüller空间Thurston边界中的无穷远星。对于Thurston度量，我们证明对每个有限型曲面，射影测度叶状结构的星恰好是其零集，扩展了Liu-Shi关于闭曲面的定理，且基于星与星一致；对于Teichmüller度量，我们证明射影测度叶状结构的基于星和星均与其两步零集重合，该集合可严格大于零集，否定了Karlsson的一个猜想。
英文摘要
We study the stars at infinity in the Thurston boundary of Teichmüller space for the Thurston and Teichmüller metrics. For the Thurston metric, we prove that for every finite-type surface, the star of a projective measured lamination is exactly its zero set, extending a theorem of Liu-Shi from closed surfaces. Moreover, the based star agrees with the star. For the Teichmüller metric, we show that both the based star and the star of a projective measured lamination coincide with its two-step zero set. This set can be strictly larger than the zero set, disproving a conjecture of Karlsson.
