Pants Decompositions of Random Surfaces

Larry Guth, Hugo Parlier, Robert Young

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1069-1090
Number of pages22
JournalGeometric and Functional Analysis
Volume21
Issue number5
DOIs
StatePublished - Oct 2011

Fingerprint

Random Surfaces
Hyperbolic Metric
Decompose
Hyperbolic Surface
Gluing
Moduli Space
Triangle
Euclidean
Genus
Metric
Curve
Unit
Context
Form

Keywords

  • Bers' constants
  • Riemann surfaces
  • simple closed geodesics
  • Teichmüller and moduli spaces

ASJC Scopus subject areas

  • Geometry and Topology
  • Analysis

Cite this

Pants Decompositions of Random Surfaces. / Guth, Larry; Parlier, Hugo; Young, Robert.

In: Geometric and Functional Analysis, Vol. 21, No. 5, 10.2011, p. 1069-1090.

Research output: Contribution to journalArticle

Guth, Larry ; Parlier, Hugo ; Young, Robert. / Pants Decompositions of Random Surfaces. In: Geometric and Functional Analysis. 2011 ; Vol. 21, No. 5. pp. 1069-1090.
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