The Area of Convex Projective Surfaces and Fock-Goncharov Coordinates

TL;DR

This paper establishes a lower bound for the area of convex projective surfaces of genus g, linking it to triangle invariants and Fock-Goncharov coordinates, thus connecting geometric and coordinate-based descriptions.

Contribution

It provides a new lower bound for the area of convex projective surfaces using Fock-Goncharov coordinates and triangle invariants, bridging geometric and algebraic perspectives.

Findings

Lower bound for surface area involving triangle invariants

Connection between geometric area and Fock-Goncharov coordinates

Explicit formula relating area to triangle invariants

Abstract

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