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.
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A Llarull-type rigidity result for scalar curvature holds on odd-dimensional Riemannian spin manifolds with cone-like singularities via twisted Dirac operators and spectral flow.
Derives sufficient conditions for non-rigidity of extremal metrics involving scalar curvature and supplies examples of manifolds satisfying them.
citing papers explorer
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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.
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Lipschitz rigidity for scalar curvature on singular manifolds in odd dimensions
A Llarull-type rigidity result for scalar curvature holds on odd-dimensional Riemannian spin manifolds with cone-like singularities via twisted Dirac operators and spectral flow.
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Extremal metrics involving scalar curvature
Derives sufficient conditions for non-rigidity of extremal metrics involving scalar curvature and supplies examples of manifolds satisfying them.