  The goal of this paper is to study Yamabe flow on a complete Riemannian
manifold of bounded geometry with possibly infinite volume. In the case of
infinite volume, standard volume normalization of the Yamabe flow fails and the
flow may not converge. Instead, we consider a curvature normalized Yamabe flow,
and assuming negative scalar curvature, prove its long-time existence and
convergence. This extends the results of Su\'arez-Serrato and Tapie to a
non-compact setting. In the appendix, we specify our analysis of a particular
example of manifolds with bounded geometry, namely manifolds with fibered
boundary metric. In this case, we obtain stronger estimates for the short-time
solution using microlocal methods.
