论文标题
双曲线穿刺球没有算术收缩期最大化器
Hyperbolic punctured spheres without arithmetic systole maximizers
论文作者
论文摘要
我们找到了收缩期长度的界限 - 最短的，最短的，非外围闭合曲线 - 算术刺穿的球体带有$ n $ cusps，$ n = 4 $ th $ n = 12 $，其中一些以前是由于schmutz而闻名的。使用此类表面和平面三角剖分之间的对应关系显示。我们表明，对于$ n = 7,10,11 $，算术表面无法达到最大的收缩长度。
We find bounds for the length of the systole -- the shortest essential, non-peripheral closed curve -- for arithmetic punctured spheres with $n$ cusps, for $n=4$ through $n=12$, some of which were previously known due to Schmutz. This is shown using a correspondence between such surfaces and planar triangulations. We show that for $n=7,10,11$, arithmetic surfaces do not achieve the maximal systole length.
