Rigidity of Teichmuller space

• 成果类型: Article
• 署名作者: Daskalopoulos, Georgios; Mese, Chikako
• 署名单位: Brown University; Johns Hopkins University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-01020-2
• 发表日期: 2021
• 页码: 791-916
• 关键词: moduli space; canonical metrics; petersson; compact; superrigidity; extension; CURVATURE; geometry

摘要

We prove the holomorphic rigidity conjecture of Teichmuller space which loosely speaking states that the action of the mapping class group uniquely determines theTeichmuller space as a complex manifold. The method of proof is through harmonicmaps. We prove that the singular set of a harmonic map from a smooth n-dimensional Riemannian domain to theWeil-Petersson completion T of Teichmuller space has Hausdorff dimension at most n - 2, and moreover, u has certain decay near the singular set. Combining this with the earlier work of Schumacher, Siu and Jost-Yau, we provide a proof of the holomorphic rigidity of Teichmuller space. In addition, our results provide as a byproduct a harmonicmaps proof of both the high rank and the rank one super-rigidity of the mapping class group proved via other methods by Farb-Masur and Yeung.