  Our main result is that if a generic convex domain in $\R^n$ collapses to a
domain in $\R^{n-1}$, then the difference between the first two Dirichlet
eigenvalues of the Euclidean Laplacian, known as the fundamental gap, diverges.
The boundary of the domain need not be smooth, merely Lipschitz continuous. To
motivate the general case, we first prove the analogous result for triangular
and polygonal domains. In so doing, we prove that the first two eigenvalues of
triangular domains cannot be polyhomogeneous on the moduli space of triangles
without blowing up a certain point. Our results show that the gap generically
diverges under one dimensional collapse and is bounded only if the domain is
sufficiently close to a rectangle in two dimensions or a cylinder in higher
dimensions.
