The Weil-Petersson geometry of the moduli of curves for large genus

来源 :2017几何分析和概率研讨会 | 被引量 : 0次 | 上传用户:hao68
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  We study the systole function along Weil-Petersson geodesics.We show that the square root of the systole function is uniform Lipschitz on the Teichmuller space endowed with the Weil-Petersson metric.As an application,we study the growth of the Weil-Petersson inradius of the moduli space of Riemann surfaces of genus $g$ with $n$ punctures as a function of $g$ and $n$.We show that the Weil-Petersson inradius is comparable to $\sqrt{\ln{g}}$ with respect to $g$,and is comparable to $1$ with respect to $n$.
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