Pants Decompositions of Random Surfaces
Pants Decompositions of Random Surfaces
复制标题
随机表面的裤子分解
DOI：
10.1007/s00039-011-0131-x
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发表时间：
2010
影响因子：
2.2
通讯作者：
Robert Young
中科院分区：
文献类型：
--
作者：
L. Guth;H. Parlier;Robert Young
我们的目标是在两个不同的背景下展示“随机的”表面有大的裤子分解。首先，我们证明了亏格g的双曲曲面的任何裤子分解都需要总长度至少为G7/6−ε的曲线。此外，我们还证明了这个界对于配备Weil-Petersson体积形式的双曲度量的模空间中的大多数度量都成立。然后，我们考虑通过随机地将欧几里得三角形(单位边长)粘合在一起而得到的曲面，并证明这些曲面具有相同的性质。
Our goal is to show, in two different contexts, that “random” surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus g for which any pants decomposition requires curves of total length at least g7/6−ε. Moreover, we prove that this bound holds for most metrics in the moduli space of hyperbolic metrics equipped with the Weil–Petersson volume form. We then consider surfaces obtained by randomly gluing euclidean triangles (with unit side length) together and show that these surfaces have the same property.