论文标题
在双曲表面的脸颊常数上
On Cheeger constants of hyperbolic surfaces
论文作者
论文摘要
由于金刚毛，这是一个众所周知的结果，即大型$ d $ regarbular图的最大cheeger常数不能接近$ d $ regratular tree树的cheeger常数。我们类似地证明，大属的闭合双曲线表面的脸颊常数从上面限制为$ 2/π\约0.63 ... $，严格小于双曲机平面的cheeger常数。该证明使用基于泊松的随机结构，其表面具有消失的强度。
It is a well-known result due to Bollobas that the maximal Cheeger constant of large $d$-regular graphs cannot be close to the Cheeger constant of the $d$-regular tree. We prove analogously that the Cheeger constant of closed hyperbolic surfaces of large genus is bounded from above by $2/π\approx 0.63...$ which is strictly less than the Cheeger constant of the hyperbolic plane. The proof uses a random construction based on a Poisson--Voronoi tessellation of the surface with a vanishing intensity.
