Pants Decompositions of Random Surfaces
By Larry Guth, H. Parlier, Robert Young. 2010
59 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ce97f55337af4716ae922a2e5a08b144aeab7372
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Planar stochastic hyperbolic triangulations (2016, background): “Some results in the literature already indicate that large triangulations of high genus should be locally planar such as [24, 28] or the paper [5] in the case of unicellular maps.”