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Llarull's theorem on punctured sphere with $L^\infty$ metric
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abstract
The classical Llarull theorem states that a smooth metric on $n$-sphere cannot have scalar curvature no less than $n(n-1)$ and dominate the standard spherical metric at the same time unless it is the standard spherical metric. In this work, we prove that Llarull's rigidity theorem holds for $L^{\infty}$ metrics on spheres with finitely many points punctured. This is related to a question of Gromov.
Forward citations
Cited by 2 Pith papers
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A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities
For spin manifolds with iterated conical singularities, scalar-mean curvature comparison forces equality and rigidity, and nonnegative scalar curvature implies nonnegative ADM mass.
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Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds
Odd-dimensional Llarull rigidity holds for Lipschitz area non-increasing maps and for manifolds with cone-like singularities, proved via spherical suspension and abstract cone operators.
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