  We consider the solution operator for the wave equation on the flat Euclidean
cone over the circle of radius $\rho > 0$, the manifold $\mathbb{R}_+ \times
\mathbb{R} / 2 \pi \rho \mathbb{Z}$ equipped with the metric $\g(r,\theta) =
dr^2 + r^2 d\theta^2$. Using explicit representations of the solution operator
in regions related to flat wave propagation and diffraction by the cone point,
we prove dispersive estimates and hence scale invariant Strichartz estimates
for the wave equation on flat cones. We then show that this yields
corresponding inequalities on wedge domains, polygons, and Euclidean surfaces
with conic singularities. This in turn yields well-posedness results for the
nonlinear wave equation on such manifolds. Morawetz estimates on the cone are
also treated.
