An orientable 3-manifold with positive scalar curvature decaying at rate C > 2/3 must be a connected sum of spherical manifolds and S^2 x S^1 pieces, and the threshold 2/3 is optimal.
A generalization of the G eroch conjecture with arbitrary ends
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Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay
An orientable 3-manifold with positive scalar curvature decaying at rate C > 2/3 must be a connected sum of spherical manifolds and S^2 x S^1 pieces, and the threshold 2/3 is optimal.