Stability of the Riemannian positive mass theorem in all dimensions

Gaoming Wang; Yiyue Zhang

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arXiv · 2609.01540

Stability of the Riemannian positive mass theorem in all dimensions

Gaoming Wang·Yiyue Zhang

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Abstract

We prove stability of the Riemannian positive mass theorem in all dimensions, extending the Dong-Song stability theorem. For a sequence of complete asymptotically flat manifolds with nonnegative scalar curvature and ADM masses tending to zero, excising domains whose boundary areas tend to zero yields exterior regions converging to Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof constructs global coordinates from minimal graphs and controls their Hessians using scalar solutions of the conformal Laplace equation on the associated graph metrics.

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Gaoming Wang, Yiyue Zhang. 2026-09-21. Stability of the Riemannian positive mass theorem in all dimensions. https://arxiv.org/abs/2609.01540

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