Stars at infinity in the Thurston boundary

Meenakshy Jyothis; Jing Tao

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arXiv · 2608.22461

Stars at infinity in the Thurston boundary

Meenakshy Jyothis·Jing Tao

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Abstract

We study the stars at infinity in the Thurston boundary of Teichm\"uller space for the Thurston and Teichm\"uller 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 Teichm\"uller 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.

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BibTeX RIS

Meenakshy Jyothis, Jing Tao. 2026-08-23. Stars at infinity in the Thurston boundary. https://arxiv.org/abs/2608.22461

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