  In this paper, we investigate the topological obstruction problem for
positive scalar curvature and uniformly positive scalar curvature on open
manifolds. We present a definition for open Schoen-Yau-Schick manifolds and
prove that there is no complete metric with positive scalar curvature on these
manifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy,
which are expected to admit no complete metrics with uniformly positive scalar
curvature.
