Surjectivity cannot replace nonzero degree in Llarull's theorem for n≥3 but can for n=2; the Ricci-curvature version holds in all dimensions.
B.: The classification of simply connected manifolds of positive scalar curvature
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The degree condition in Llarull's theorem on scalar curvature rigidity
Surjectivity cannot replace nonzero degree in Llarull's theorem for n≥3 but can for n=2; the Ricci-curvature version holds in all dimensions.