The Area of Convex Projective Surfaces and Fock-Goncharov Coordinates

Abstract

The area of a convex projective surface of genus $g\ge 2$ is at least $(g-1){\pi }^2/2+\Vert \tau {\Vert }^2/8$ where $\tau =(\log t_i)$ is the vector of triangle invariants of Bonahon-Dreyer and $t_i$ are the Fock-Goncharov triangle coordinates.

arXiv commentIntroduction revised. References added. After the first version of this paper was posted the authors learned of arXiv:math/0312163 [math.DG]. There, the authors show that the Hausdorff area of an ideal triangle in a convex domain is bounded below. The point of this paper is the relationship of p-area to Fock-Goncharov coordinates. The text and the title have been changed to reflect that