On the number and location of short geodesics in moduli space
On the number and location of short geodesics in moduli space
复制标题
模空间中短测地线的数量和位置
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
D. Margalit
中科院分区：
文献类型：
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作者：
C. Leininger;D. Margalit
亏格为g的黎曼曲面的模空间Rg中的闭Teichmüller测地线称为L-short，如果它的长度至多为L/g。我们证明了，对于任意L>0，存在R> R>0，与g无关，从而使得L-g中的L-短测地线都位于R-薄部分和L-厚部分的交点上。我们还估计了在g中L-短测地线的数量，通过g中多项式的次数依赖于L并随着L趋于无穷大来从上到下限制它。
A closed Teichmüller geodesic in the moduli space ℳg of Riemann surfaces of genus g is called L‐short if it has length at most L/g. We show that, for any L>0, there exist R>ϵ>0, independent of g, so that the L‐short geodesics in ℳg all lie in the intersection of the ϵ‐thick part and the R‐thin part. We also estimate the number of L‐short geodesics in ℳg, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.