Convergence of Siegel–Veech constants
Convergence of Siegel–Veech constants
复制标题
西格尔-维奇常数的收敛性
DOI：
10.1007/s10711-018-0332-7
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发表时间：
2016
影响因子：
0.5
通讯作者：
B. Dozier
中科院分区：
文献类型：
--
作者：
B. Dozier
We show that for any weakly convergent sequence of ergodic SL2(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SL_2(\mathbb {R})$$\end{document}-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel–Veech constants converge to the Siegel–Veech constant of the limit measure. Together with a measure equidistribution result due to Eskin–Mirzakhani–Mohammadi, this yields the (previously conjectured) convergence of sequences of Siegel–Veech constants associated to Teichmüller curves in genus two. The proof uses a recurrence result closely related to techniques developed by Eskin–Masur. We also use this recurrence result to get an asymptotic quadratic upper bound, with a uniform constant depending only on the stratum, for the number of saddle connections of length at most R on a unit-area translation surface.
We show that for any weakly convergent sequence of ergodic SL2(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SL_2(\mathbb {R})$$\end{document}-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel–Veech constants converge to the Siegel–Veech constant of the limit measure. Together with a measure equidistribution result due to Eskin–Mirzakhani–Mohammadi, this yields the (previously conjectured) convergence of sequences of Siegel–Veech constants associated to Teichmüller curves in genus two. The proof uses a recurrence result closely related to techniques developed by Eskin–Masur. We also use this recurrence result to get an asymptotic quadratic upper bound, with a uniform constant depending only on the stratum, for the number of saddle connections of length at most R on a unit-area translation surface.
影响因子：
3.9
作者：
Chen, Dawei;Moeller, Martin;Zagier, Don
通讯作者：
Zagier, Don