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Veech Surfaces and Simple Closed Curves by Forester, Max; Tang, Robert; Tao, Jing is a scholarly article available to read on EtoBox.

What is Veech Surfaces and Simple Closed Curves about?

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.

Author

Forester, Max; Tang, Robert; Tao, Jing

Published

2016

Language

EN