论文标题
通用翻译表面的水平差距的收缩率
Shrinking rates of horizontal gaps for generic translation surfaces
论文作者
论文摘要
平面中的多边形给出了翻译表面，侧面由翻译确定，以创建一个封闭的Riemann表面，其平坦的结构远离有限的许多单数点。理解表面上的大地测量流涉及了解马鞍连接。鞍座连接是从这些单数点开始和结束的大地测量，并且与平面的离散子集有关。为了衡量最多最多$ r $的鞍座连接的行为，我们将精确的衰减率为$ r \ to \ infty $，对于两个几乎水平的鞍座连接之间的角度差异。
A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many singular points. Understanding geodesic flow on a surface involves understanding saddle connections. Saddle connections are the geodesics starting and ending at these singular points and are associated to a discrete subset of the plane. To measure the behavior of saddle connections of length at most $R$, we obtain precise decay rates as $R\to \infty$ for the difference in angle between two almost horizontal saddle connections.
