论文标题
联系Instantons，反接触的互动和Shelukhin猜想的证明
Contact instantons, anti-contact involution and proof of Shelukhin's conjecture
论文作者
论文摘要
在本文中，我们证明了Shelukhin在任何封闭的触点歧管$（q，ξ）$上的翻译点上的猜想，该$（Q，ξ）$读到，对于任何功能的选择，$ h = h = h（t，x）$和触点表格$λ$ contactomorphism $ψ_h^1 $ a^1 $带有桑德（Sandon）的翻译点，每当桑德（Sandon）的含义，每当桑德（Sandon）的意义上， \ leq t（λ，m）$$持有案例。主要的几何分析工具是[OHC]中通过触觉差异性的传统边界条件使用的边界接触式工具。在此过程中，我们利用接触产品的功能构建，该构造具有参与对称性，并与涉及对称性相关的汉密尔顿几何形状。这种参与对称性在我们的证明中起着基本作用，结合了联系Instantons的分析。
In this paper, we prove Shelukhin's conjecture on the translated points on any closed contact manifold $(Q,ξ)$ which reads that for any choice of function $H = H(t,x)$ and contact form $λ$ the contactomorphism $ψ_H^1$ carries a translated point in the sense of Sandon, whenever the inequality $$ \|H\| \leq T(λ,M) $$ holds the case. Main geometro-analytical tools are those of bordered contact instantons employed in [Ohc] with Legendrian boundary condition via the Legendrianization of contact diffeomorphisms. Along the way, we utilize the functorial construction of the contact product that carries an involutive symmetry and develop relevant contact Hamiltonian geometry with involutive symmetry. This involutive symmetry plays a fundamental role in our proof in combination with the analysis of contact instantons.
