Israel Journal of Mathematics

We study the SL(2,R)-infimal lengths of simple closed curves on half-translation 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.

- pdf file (16 pages)
- main article page at Springer