  In this article we study the first eigenvalues of closed Riemann surfaces for
large genus. We show that for every closed Riemann surface $X_g$ of genus $g$
$(g\geq 2)$, the first eigenvalue of $X_g$ is greater than
$\frac{\mathcal{L}_1(X_g)}{g^2}$ up to a uniform positive constant
multiplication. Where $\mathcal{L}_1(X_g)$ is the shortest length of multi
closed curves separating $X_g$. Moreover,we also show that this new lower bound
is optimal as $g \to \infty$.
