模空间厚子集的相对形状
Relative shapes of thick subsets of moduli space
摘要：
一个亏格为$g\ge 2$的闭双曲曲面可以沿着最短的闭测地线被分解成一对裤子，如果这些曲线足够短（并且长度均匀地有界远离0），那么曲面的几何形状基本上是由裤子分解的组合学决定的。这些组合是由一个三价图决定的，所以我们称这样的曲面为{ \em三价}。在本文中，在第一次尝试了解的“形状”的子集$\ts$的模空间组成的表面，其systoles填充，我们比较它的度量，渐近g，与一组$\tri$的三价表面。作为我们的主要结果，我们发现集合$\ts \cap \tri$在$\ts$中是度量“稀疏”的（这里我们给$\moduli$配备Thurston或Teichmüller度量）.
英文摘要：
A closed hyperbolic surface of genus $g\ge 2$ can be decomposed into pairs of pants along shortest closed geodesics and if these curves are sufficiently short (and with lengths uniformly bounded away from 0), then the geometry of the surface is essentially determined by the combinatorics of the pants decomposition. These combinatorics are determined by a trivalent graph, so we call such surfaces {\em trivalent}. In this paper, in a first attempt to understand the "shape" of the subset $\ts$ of moduli space consisting of surfaces whose systoles fill, we compare it metrically, asymptotically in g, with the set $\tri$ of trivalent surfaces. As our main result, we find that the set $\ts \cap \tri$ is metrically "sparse" in $\ts$ (where we equip $\moduli$ with either the Thurston or the Teichmüller metric).
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