Intrinsic-flat noncancellation conjecture for three-manifolds with positive scalar curvature

A converging sequence of three-dimensional Riemannian manifolds means a sequence of three-dimensional Riemannian manifolds converging in the intrinsic flat sense. The sequence has positive scalar curvature if every manifold in it has positive scalar curvature, has a uniform lower bound on volume if there is a positive constant bounding their volumes below, and has no interior minimal surfaces if none of the manifolds contains an interior minimal surface.

Intrinsic-flat noncancellation conjecture. A converging sequence of three-dimensional Riemannian manifolds with positive scalar curvature, a uniform lower bound on volume, and no interior minimal surfaces converges without cancellation to a nonzero integral current space.

This conjecture concerns conditions preventing cancellation in intrinsic flat limits. It was motivated by examples of positive-scalar-curvature manifolds whose intrinsic flat limits collapse to the zero integral current space when increasingly dense tunnels are present; the stated noncancellation result remains unresolved in the supplied source.