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Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities

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arxiv 2310.13285 v2 pith:Z6MWON65 submitted 2023-10-20 math.DG

Xianzhe Dai , Yukai Sun , Changliang Wang This is my paper · ORCID
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keywords masssingularitiesconicalmanifoldspositiveasymptoticallyflathorn
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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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  1. Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

    math.DG 2025-05 accept novelty 7.0 of 10

    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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