The Area of Convex Projective Surfaces and Fock-Goncharov Coordinates

preprint2016arXivOpen access

Abstract

The area of a convex projective surface of genus g≥2g\ge 2 is at least (g−1)π2/2+∥τ∥2/8(g-1)π^2/2+\|τ\|^2/8 where τ=(log⁡ti)τ=(\log t_i) is the vector of triangle invariants of Bonahon-Dreyer and tit_i are the Fock-Goncharov triangle coordinates.

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