In: Geometric and Functional Analysis, 2011, vol. 21, no. 5, p. 1069-1090
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In: Geometric and functional analysis, 2012, vol. 22, no. 1, p. 37-73
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directions.First, we find bounds on the lengths of homologically independent curves on closed Riemannian surfaces. As a consequence, we show that for any l Î (0, 1) there exists a constant C λ such that...
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In: Geometric and Functional Analysis, 2011, vol. 21, no. 5, p. 1069-1090
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 modulispace of hyperbolic metrics equipped with the Weil–Petersson volume...
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