论文标题
基本光谱不变和定量闭合引理三个manifolds
Elementary spectral invariants and quantitative closing lemmas for contact three-manifolds
论文作者
论文摘要
在上一篇论文中，我们使用了受到点约束的全态曲线的最大阵线能量，并避免使用Seiberg-Witten理论。在本文中，我们使用该结构的一种变体来定义触点三元模型的ECH频谱的替代方案。替代频谱在三个维度上具有REEB动力学的应用。特别是，我们适应了先前与Edtmair的联合论文的想法，以在三个维度上为Reeb载体场获得定量的关闭引理。在非理性椭圆形的示例中，我们获得了尖锐的定量闭合引理。
In a previous paper, we defined an "elementary" alternative to the ECH capacities of symplectic four-manifolds, using max-min energy of holomorphic curves subject to point constraints, and avoiding the use of Seiberg-Witten theory. In the present paper we use a variant of this construction to define an alternative to the ECH spectrum of a contact three-manifold. The alternative spectrum has applications to Reeb dynamics in three dimensions. In particular, we adapt ideas from a previous joint paper with Edtmair to obtain quantitative closing lemmas for Reeb vector fields in three dimensions. For the example of an irrational ellipsoid, we obtain a sharp quantitative closing lemma.
