Rationally convex domains and singular Lagrangian surfaces in C2

• 成果类型: Article
• 署名作者: Nemirovski, Stefan; Siegel, Kyler
• 署名单位: Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Ruhr University Bochum; Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0598-4
• 发表日期: 2016
• 页码: 333-358
• 关键词: tight contact structures; TOPOLOGY; MANIFOLDS

摘要

We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in . We recall some classical obstructions and prove some deeper ones related to symplectic and contact topology. We explain the close connection to Lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces. Our proof also gives a complete characterization of Lagrangian surfaces with open Whitney umbrellas, answering a question first posed by Givental in 1986.