2023/07/06 by Xinlong Dong, Dong, Xinlong, Hrant Hakobyan +1
Mathematics · Social Sciences · #30C62 #30F60 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Global Maritime and Colonial Histories #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2307.02775
openalex publication_date 2023/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thurston boundary of the universal Teichmüller space T(\mathbbD) is the space PMLbdd(\mathbbD) of projective bounded measured laminations of \mathbbD. A geodesic ray in T(\mathbbD) is of generalized Teichmüller type if it shrinks the vertical foliation of a holomorphic quadratic differential. We provide the first examples of generalized Teichmüller rays which diverge near Thurston boundary PLMbdd(\mathbbD). Moreover, for every k≥ 1 we construct examples of rays with limit sets homeomorphic to k-dimensional cubes. For the latter result we utilize the classical Kronecker approximation theorem from number theory which states that if θ1,…,θk are rationally independent reals then the sequence (\θ1 n\,…,\θk n\) is dense in the k-torus \mathbbTk.