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.
Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities
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There has been a lot of interests in Positive Mass Theorems for singular metrics on smooth manifolds. We prove a positive mass theorem for asymptotically flat (AF) spin manifolds with isolated conical singularities or more generally horn singularities. In particular, we allow topological singularities in the space as we do not require the cross sections of the conical singularity to be spherical. Note that the negative mass Schwarzschild metric is AF with a horn singularity.
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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.