### Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one

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We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality $E\ge \left|P\right|$ holds, where $(E,P)$ is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem...

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