论文标题
与短马鞍连接的翻译表面绑定的测量
Measure bound for translation surfaces with short saddle connections
论文作者
论文摘要
我们证明，在翻译表面层上的任何Ergodic $ sl_2（r）$ - 不变的概率度量都可以满足强的规律性：具有两个非平行马鞍连接的表面的度量，最多为$ε_1，ε_2$ i是$ o（ε_1^2ε_2ε_2ε_2^ε_2^2^2）$。我们证明了一个更通用的定理，可用于任何数量的短马鞍连接。该证明使用了贝恩布里奇·奇德隆·格鲁什夫斯基 - 莫勒最近引入的地层的多尺度压实和菲利普的代数结果。
We prove that any ergodic $SL_2(R)$-invariant probability measure on a stratum of translation surfaces satisfies strong regularity: the measure of the set of surfaces with two non-parallel saddle connections of length at most $ε_1, ε_2$ is $O(ε_1^2 ε_2^2)$. We prove a more general theorem which works for any number of short saddle connections. The proof uses the multi-scale compactification of strata recently introduced by Bainbridge-Chen-Gendron-Grushevsky-Möller and the algebraicity result of Filip.
