论文标题
在负弯曲表面上的封闭测量学的比较定理
Comparison theorems for closed geodesics on negatively curved surfaces
论文作者
论文摘要
在本说明中，我们提出了新的渐近估计，比较了（可变）负截面曲率的表面上封闭的大地测量学的单词长度和大地测量长度。特别是，我们提供了这两个重要数量的平均比较，并获得精确的统计结果，包括中心限制定理和局部限制定理。此外，作为推论，我们还提高了R. Sharp和第二作者的渐近公式。最后，我们将结果与Gekhtman，Taylor和Tiozzo的最新工作联系起来。
In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.
