Chekhanov定理综述
A survey on the Theorem of Chekhanov
摘要：
Chekhanov定理断言，在无穷远辛拓扑的自然假设下，拉格朗日子流形L具有正的位移能。它大于或等于以L为界的全纯圆盘的极小面积。这一估计是由Y.V. Chekhanov在1998年得出的。第1节给出了一个直接的证明的基础上使用的全纯曲线和它们的哈密顿扰动。在第二节中，我们定义了拉格朗日弗洛尔同调的一个滤波形式，而不对L作任何假设。通过延拓映射（2.3.2小节）或PSS映射（3.2小节），将其与Morse同调群进行比较。
英文摘要：
The theorem of Chekhanov asserts that a Lagrangian submanifold L has positive displacement energy under natural assumptions on the symplectic topology at infinity. It is greater than or equal to the minimal area of holomorphic disks bounded by L. This estimate was obtained by Y.V. Chekhanov in 1998. Section 1 presents a direct proof based on the use of holomorphic curves and their Hamiltonian perturbations. In section 2, we define a filtered version of the Lagrangian Floer homology, without any assumption on L. This is compared with the Morse homology groups, via the continuation maps (subsubsection 2.3.2) or the PSS maps (subsection 3.2).
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