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arXiv · 2110.07929

Minimizing entropy for translation surfaces

Paul Colognese·Mark Pollicott
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Abstract

In this note, we consider the entropy of unit area translation surfaces in the $SL(2, \mathbb R)$ orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices.

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Paul Colognese, Mark Pollicott. 2021-10-15. Minimizing entropy for translation surfaces. https://arxiv.org/abs/2110.07929

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