Systolic inequalities in Reeb dynamics (B03)

这个项目的目的是研究哈密顿系统的接触收缩比以及更广泛的作用谱与体积之间的关系。我们将继续研究的关键问题涉及在凸性假设下或在全局对称假设下接触收缩比的上界。答案有望阐明辛拓扑、黎曼和芬斯勒收缩几何、凸几何和台球动力学中的重要公开问题。

The aim of this project is to investigate the contact systolic ratio and more broadly the relation between the action spectrum and the volume for Hamiltonian systems. Key questions we will continue to investigate concern upper bounds for the contact systolic ratio under convexity assumptions, or under global symmetry assumptions. Answers are expected to shed light on important open problems in symplectic topology, Riemannian and Finsler systolic geometry, convex geometry and billiard dynamics.