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数学进展 - 2018, Vol. 47(1): 1-10
综述文章
关于Weinstein猜测的综述
A Survey on Weinstein Conjecture

丁岩峭
DING Yanqia

郑州大学数学与统计学院, 郑州, 河南, 450001
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 1-10
DOI: 10.11845/sxjz.2017005a


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摘要 Weinstein猜测断言辛流形的紧致切触超曲面上至少有一个周期轨道,这一猜测是辛拓扑和切触拓扑中重要的研究方向.根据方法的不同,本文综述利用变分法和伪全纯曲线方法对Weinstein猜测进行的研究.
关键词 Weinstein猜测周期轨道切触流形$J$-全纯曲线Reeb流    
Abstract:Weinstein conjecture predicts that every compact contact hypersurface in the symplectic manifold has at least one periodic orbit, and it is an important direction of research in symplectic topology and contact topology. According to the methods of the research, this note surveys the study on Weinstein conjecture using variational method and pseudo-holomorphic curves method.
Key wordsWeinstein conjecture    periodic orbit    contact manifold    $J$-holomorphic curves    Reeb flow
PACS:  O186  
  O192  
基金资助:郑州大学青年教师启动基金(No. 32210405).
通讯作者: E-mail: yqding@zzu.edu.cn   
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