Quasi-Isometric Rigidity of Teichmüller Space: An Expository Survey of the Eskin-Masur-Kasra Rafi Theorem

Quasi-Isometric Rigidity of Teichmüller Space (A Survey) This is an expository survey of a landmark rigidity theorem for Teichmüller space, proved by Eskin, Masur, and Kasra Rafi. The theorem states that, with a short list of low-complexity exceptions, every quasi-isometry of Teichmüller space (with the Teichmüller metric) is within bounded distance of an isometry. The survey summarizes the theorem statement, the architecture of the proof, and places it within the broader literature on quasi-isometric rigidity of symmetric spaces and non-positively curved spaces. It is aimed at readers with a background in geometric group theory but not necessarily in Teichmüller theory.