标题： 随机复数曲线的Cheeger常数的下界 显示英文标题

标题： Lower bound for the Cheeger constant of random complex curves

摘要： 在本文中，我们提供了随机复数曲线在$\C P^2$中的 Cheeger 常数和谱间隙的下界。 复数曲线赋予了周围 Fubini-Study 度量的限制，概率测度是由复数齐次多项式空间中的$\mathscr{L}^2$-Hermitian 乘积诱导的高斯测度，这些复数齐次多项式的次数为$d$，变量数目为$3$。 证明依赖于我们之前对随机复数曲线的长度和曲率的界限，以及复数曲线上小椭圆的等周不等式。 更一般地，我们在复射影流形内的随机复数曲线中建立了这样的下界。 显示英文摘要

摘要： In this paper, we provide a lower bound for the Cheeger constant and the spectral gap for random complex curves in $\C P^2$. The complex curve is endowed with the restriction of the ambient Fubini-Study metric, and the probability measure is the Gaussian measure induced by the $\mathscr{L}^2$-Hermitian product on the space of complex homogeneous polynomialsof degree $d$ in $3$ variables. The proof relies on our previous bounds for the systole and the curvature of random complex curves, together with an isoperimetric inequality for small ovals on complex curves. More generally, we establish such lower bounds for random complex curves within complex projective manifolds.