The boundary of an affine invariant submanifold

• 成果类型: Article
• 署名作者: Mirzakhani, Maryam; Wright, Alex
• 署名单位: Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0722-8
• 发表日期: 2017
• 页码: 927-984
• 关键词: moduli space; teichmuller-curves; orbit closures; veech surfaces; quadratic-differentials; abelian differentials; connected components; translation surfaces; DYNAMICS; genus-2

摘要

We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.