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• W2964333208 abstract "In this paper we study the systole function along Weil-Petersson geodesics. We show that the square root of the systole function is uniformly Lipschitz on Teichmuller space endowed with the Weil-Petersson metric. As an application, we study the growth of the Weil-Petersson inradius of 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 $n$. Moreover, we also study the asymptotic behavior, as $g$ goes to infinity, of the Weil-Petersson volumes of geodesic balls of finite radii in Teichmuller space. We show that they behave like $o((frac{1}{g})^{(3-epsilon)g})$ as $gto infty$, where $epsilon>0$ is arbitrary." @default.
• W2964333208 created "2019-07-30" @default.
• W2964333208 creator A5054102228 @default.
• W2964333208 date "2019-06-03" @default.
• W2964333208 modified "2023-10-18" @default.
• W2964333208 title "Growth of the Weil–Petersson inradius of moduli space" @default.
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• W2964333208 doi "https://doi.org/10.5802/aif.3272" @default.
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