论文标题
简单封闭双曲线多地点的互补子表面的形状
The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics
论文作者
论文摘要
沿着简单的闭合多对地面切割双曲表面X在互补地下上的双曲线结构。我们研究了这些子图在模量空间中的形状分布，因为边界长度延伸到无穷大，这表明它们在相应的度量色带图的相应模量空间上等于Kontsevich度量。特别是，随机子表面看起来像随机色带图，这不取决于X的初始选择。这结果增强了Mirzakhani著名的简单封闭的封闭封闭的多对数计数，用于双曲线表面。
Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to infinity, showing that they equidistribute to the Kontsevich measure on a corresponding moduli space of metric ribbon graphs. In particular, random subsurfaces look like random ribbon graphs, a law which does not depend on the initial choice of X. This result strengthens Mirzakhani's famous simple closed multi-geodesic counting theorems for hyperbolic surfaces.
