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Journal article

Pants decompositions of random surfaces

  • Guth, Larry Department of Mathematics, University of Toronto, Canada
  • Parlier, Hugo Department of Mathematics, University of Fribourg, Switzerland
  • Young, Robert Courant Institute of Mathematical Sciences, New York, USA
    23.08.2011
Published in:
  • Geometric and Functional Analysis. - 2011, vol. 21, no. 5, p. 1069-1090
Riemann surfaces
Simple closed geodesics
Bers’ constants
Teichmueller and moduli spaces
English 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 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.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/302150
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