PreprintarXiv licencearXiv
Stability of the Riemannian positive mass theorem in all dimensions
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.
Related
- Spacetime Positive Mass Theorem with Boundary for Multiple Time Dimensions
- Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds
- A continuous Positive Mass Theorem for perturbations of Euclidean space
- Rigidity of positive mass theorem with fast metric decay
- A Positive Mass Type Theorem for a Singular Toroidal Static Model
BibTeX
@misc{wang2026stability,
title = {{Stability of the Riemannian positive mass theorem in all dimensions}},
author = {Gaoming Wang and Yiyue Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01540},
eprint = {2609.01540},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01540},
}
RIS
TY - UNPB
TI - Stability of the Riemannian positive mass theorem in all dimensions
AU - Gaoming Wang
AU - Yiyue Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.01540
UR - https://arxiv.org/abs/2609.01540
AB - 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.
ER -