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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Measuring pants
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by Nhat Minh Doan, Hugo Parlier and Ser Peow Tan PDF
Trans. Amer. Math. Soc. 376 (2023), 5281-5306 Request permission


We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we deduce two results. As a first application, we show how to deduce a theorem of Thurston which states, in particular for closed hyperbolic surfaces, that if a simple length spectrum “dominates” another, then in fact the two surfaces are isometric. As a second application, we show how to find upper bounds on the number of pairs of pants of bounded length that only depend on the boundary length and the topology of the surface.
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Additional Information
  • Nhat Minh Doan
  • Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam
  • Email:
  • Hugo Parlier
  • Affiliation: Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg
  • MR Author ID: 767561
  • ORCID: 0000-0001-5618-509X
  • Email:
  • Ser Peow Tan
  • Affiliation: Department of Mathematics, National University of Singapore, Singapore
  • MR Author ID: 331663
  • ORCID: 0000-0002-2382-0656
  • Email:
  • Received by editor(s): February 26, 2020
  • Received by editor(s) in revised form: September 15, 2020, and December 9, 2020
  • Published electronically: May 17, 2023
  • Additional Notes: Research of the first author was supported by FNR PRIDE15/10949314/GSM. Research of the second author was partially supported by ANR/FNR project SoS, INTER/ANR/16/11554412/SoS, ANR-17-CE40-0033. Research of the third author was partially supported by R146-000-289-114
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 5281-5306
  • MSC (2020): Primary 32G15, 57K20, 37D20; Secondary 30F10, 30F60, 53C23, 57M50
  • DOI: