Isolation, equidistribution, and orbit closures for the SL(2,R) action on moduli space

• 成果类型: Article
• 署名作者: Eskin, Alex; Mirzakhani, Maryam; Mohammadi, Amir
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.182.2.7
• 发表日期: 2015
• 页码: 673-721
• 关键词: unipotent flows; invariant-measures; measure rigidity; asymptotics; SUBGROUPS; BOUNDARY; GROWTH

摘要

We prove results about orbit closures and equidistribution for the SL(2, R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure classification theorem of the first two authors and a certain isolation property of closed SL(2, R) invariant manifolds developed in this paper.