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Positive mass theorem for asymptotically flat manifolds with isolated conical singularities

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arxiv 2401.07186 v1 pith:FUNYESXR submitted 2024-01-14 math.DG

Xianzhe Dai , Yukai Sun , Changliang Wang This is my paper · ORCID
classification math.DG
keywords conicalflatisolatedmanifoldsmasspositivesingularitiestheorem
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We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we use the conformal blow up technique which dates back to Schoen's final resolution of the Yamabe conjecture.

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  1. A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities

    math.DG 2025-06 conditional novelty 7.0 of 10

    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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