Reference : Measuring Pants
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/42494
Measuring Pants
English
Doan, Nhat Minh mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Parlier, Hugo mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Tan, Ser Peow []
10-Feb-2020
1
19
No
[en] Geometric identities ; hyperbolic surfaces ; pairs of pants
[en] 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.
Researchers ; Professionals ; Students ; General public ; Others
http://hdl.handle.net/10993/42494
19 pages, 2 figures
https://arxiv.org/abs/2002.02738

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