Title: C 0, C 1 limit theorems for
total scalar curvatures
Abstract: We give some C 0, or C 1 limit
theorems for total scalar curvatures. Specifically, we show that
under some assumptions, the lower bound of the total scalar curvatures
on a closed manifold is preserved under the C 0, or C
1 convergence of the Riemannian metrics. We also give some
counterexamples to the above theorems on some open manifolds.