Preservation of nonnegative scalar curvature under SWIF with a MinA noncollapsing hypothesis

Determine whether, assuming the MinA(M_j)\ge A_0>0 noncollapsing condition, Sormani–Wenger intrinsic flat convergence of 3-dimensional Riemannian manifolds (M_j^3, g_j) with nonnegative scalar curvature to a smooth Riemannian manifold (M_0^3, g_0) ensures that (M_0^3, g_0) has nonnegative scalar curvature.

Background

The MinA hypothesis rules out collapsing via thin tunnels and other pathological behaviors that can invalidate scalar curvature properties in limits. The authors indicate that with MinA, tunneling-based counterexamples are prevented, suggesting MinA could be a sufficient noncollapsing condition for preserving nonnegative scalar curvature in the limit.

They also note that proving this in full generality would be challenging and propose examining the VADB convergence notion of Allen–Perales–Sormani as an easier case that implies SWIF convergence.