Veech surfaces and simple closed curves
Geometric Topology
2017-01-11 v2 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1605.01772,
title = {Veech surfaces and simple closed curves},
author = {Max Forester and Robert Tang and Jing Tao},
journal= {arXiv preprint arXiv:1605.01772},
year = {2017}
}
Comments
12 pages. v2: added proof of continuity of infimal length functions on quadratic differential space; 16 pages, one figure; to appear in Israel J. Math