关于Hessel几何中的内射半径
On the injectivity radius in Hofer's geometry
摘要：
在本说明中，我们考虑以下猜想：给定任何闭辛流形$M$，存在一个足够小的实正数$ρ$，使得以$M$的哈密尔顿同态群上的恒等式为中心的哈密尔顿度量中的半径为$M$的开球是可收缩的，收缩发生在那个球里--这是猜想的强版本--或者在$M$的哈密顿同形的周围群里--这是猜想的弱版本。我们证明了几个结果，支持弱形式的猜想。
英文摘要：
In this note we consider the following conjecture: given any closed symplectic manifold $M$, there is a sufficiently small real positive number $ρ$ such that the open ball of radius $ρ$ in the Hofer metric centered at the identity on the group of Hamiltonian diffeomorphisms of $M$ is contractible, where the retraction takes place in that ball -- this is the strong version of the conjecture -- or inside the ambient group of Hamiltonian diffeomorphisms of $M$ -- this is the weak version of the conjecture. We prove several results that support that weak form of the conjecture.
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