吴云辉专题学术报告
2021-04-24 来源:数学科学研究中心活动地点:CMS 201
活动类型:学术报告
主讲人:吴云辉
活动时间:2021-04-25 14:00:00--2021-04-25 15:00:00
活动内容:
吴云辉专题学术报告
报告题目:Optimal lower bounds for first eigenvalues of Riemann surfaces for large genus
报告人:吴云辉(清华大学)
时间:2021年4月25日(周日)下午2点
地点:数学中心201教室
Abstract:In this article we study the first eigenvalues of closed hyperbolic surfaces for large genus. We show that for every closed hyperbolic surface $X_g$ of genus $g$ $(g\geq 2)$, the first eigenvalue of $X_g$ is greater than $\frac{L_1(X_g)}{g^2}$ up to a uniform positive constant multiplication. Where $L_1(X_g)$ is the shortest length of simple closed multi-geodesics separating $X_g$. Moreover,we also show that this new lower bound is optimal as $g \to \infty$. This is a joint work with Yuhao Xue.