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- W2891506069 abstract "In this article we study the asymptotic behavior of small eigenvalues of Riemann surfaces for large genus. We show that for any positive integer $k$, as the genus $g$ goes to infinity, the smallest $k$-th eigenvalue of Riemann surfaces in any thick part of moduli space of Riemann surfaces of genus $g$ is uniformly comparable to $frac{1}{g^2}$ in $g$. In the proof of the upper bound, for any constant $epsilon>0$, we will construct a closed Riemann surface of genus $g$ in any $epsilon$-thick part of moduli space such that it admits a pants decomposition whose boundary curves all have length equal to $epsilon$, and the number of separating systole curves in this surface is uniformly comparable to $g$." @default.
- W2891506069 created "2018-09-27" @default.
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- W2891506069 date "2021-12-08" @default.
- W2891506069 modified "2023-10-14" @default.
- W2891506069 title "Small eigenvalues of closed Riemann surfaces for large genus" @default.
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- W2891506069 doi "https://doi.org/10.1090/tran/8608" @default.
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