Punctured holomorphic curves and Lagrangian embeddings
Punctured holomorphic curves and Lagrangian embeddings
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DOI：
10.1007/s00222-017-0767-8
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发表时间：
2018-04-01
影响因子：
3.1
通讯作者：
Mohnke, K.
中科院分区：
文献类型：
--
作者：
Cieliebak, K.;Mohnke, K.
利用全纯曲线的颈部拉伸论证，在非正曲率的拉格朗日子流形上得到了具有边界的小面积马氏类辛盘。应用包括线性辛空间中拉格朗日环面马斯洛夫类上的Audin猜想的证明，一个新的辛容量的构造，拉格朗日嵌入到无规辛流形中的阻碍，Arnold弦猜想的一个定量版本，以及Weinstein邻域大小的估计。具有切线条件的穿孔全纯曲线的相关模空间的横向性是其主要技术成分。
We use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive curvature. Applications include the proof of Audin's conjecture on the Maslov class of Lagrangian tori in linear symplectic space, the construction of a new symplectic capacity, obstructions to Lagrangian embeddings into uniruled symplectic manifolds, a quantitative version of Arnold's chord conjecture, and estimates on the size of Weinstein neighbourhoods. The main technical ingredient is transversality for the relevant moduli spaces of punctured holomorphic curves with tangency conditions.