  The fundamental gap conjecture was recently proven by Andrews and
Clutterbuck: for any convex domain in $\R^n$ normalized to have unit diameter,
the difference between the first two Dirichlet eigenvalues of the Laplacian is
bounded below by that of the interval. In this work, we focus on the moduli
spaces of simplices in all dimensions, and later specialize to the moduli space
of Euclidean triangles. Our first theorem is a compactness result for the gap
function on the moduli space of simplices in any dimension. Our second main
result verifies a recent conjecture of Antunes-Freitas: for any Euclidean
triangle normalized to have unit diameter, the fundamental gap is uniquely
minimized by the equilateral triangle.
