Veech surfaces and simple closed curves

Max Forester*, Robert Tang, Jing Tao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We study the SL(2, ℝ)-infimal lengths of simple closed curves on halftranslation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the “no small virtual triangles” theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spectrum of a half-translation surface either has a gap above zero or is dense in a neighborhood of zero. These results make use of the auxiliary polygon associated to a curve on a half-translation surface, as introduced by Tang and Webb.

Original languageEnglish
Pages (from-to)323-342
Number of pages20
JournalIsrael Journal of Mathematics
Issue number1
Publication statusPublished - 1 Feb 2018
Externally publishedYes


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