  This article presents an analysis of the normalized Yamabe flow starting at
and preserving a class of compact Riemannian manifolds with incomplete edge
singularities and negative Yamabe invariant. Our main results include
uniqueness, long-time existence and convergence of the edge Yamabe flow
starting at a metric with everywhere negative scalar curvature. Our methods
include novel maximum principle results on the singular edge space without
using barrier functions. Moreover, our uniform bounds on solutions are
established by a new ansatz without in any way using or redeveloping
Krylov-Safonov estimates in the singular setting. As an application we obtain a
solution to the Yamabe problem for incomplete edge metrics with negative Yamabe
invariant using flow techniques. Our methods lay groundwork for studying other
flows like the mean curvature flow as well as the porous medium equation in the
singular setting.
