Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space
Name
39_2023_656_ReferencePDF.pdf
Size
1.15 MB
Format
Adobe PDF
Checksum (MD5)
ca90735a1dfdbce8ce9161fb18591148
Author(s)
Vasudevan, Sahana
Date Issued
March 4, 2024
Journal
Geometric and Functional Analysis
Publisher
Springer International Publishing
Citation
Vasudevan, S. Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space. Geom. Funct. Anal. 34, 529–630 (2024).
Version
Author's final manuscript
Abstract
Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover asked how triangulated surfaces are distributed in the moduli space of Riemann surfaces as the genus tends to infinity. Mirzakhani raised this question in her 2010 ICM address. We show that in the large genus case, triangulated surfaces are well distributed in moduli space in a fairly strong sense. We do this by proving upper and lower bounds for the number of triangulated surfaces lying in a Teichmüller ball in moduli space. In particular, we show that the number of triangulated surfaces lying in a Teichmüller unit ball is at most exponential in the number of triangles, independent of the genus.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-023-00656-5
