PreprintarXiv licencearXiv
Rigidity of positive mass theorem with fast metric decay
Abstract
In this work, we consider metrics on Euclidean space with nonnegative scalar curvature and rapid decay at infinity. We show that, in dimensions four and higher, any such metric is necessarily flat if its decay rate exceeds that of the Schwarzschild metric. This complements recent works by Mazurowski-Yao and You-Zhang, thereby establishing Gromov's conjecture on the rigidity of the positive mass theorem under fast metric decay in all dimensions. Our method also extend naturally to weakly asymptotically flat manifolds.
Related
- Biholomorphic rigidity and symmetry breaking for domains with Bergman metric of constant positive holomorphic sectional curvature
- Positive mass and rigidity for asymptotically flat tangent bundles
- Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds
- A continuous Positive Mass Theorem for perturbations of Euclidean space
- Stability of the Riemannian positive mass theorem in all dimensions
BibTeX
@misc{chu2026rigidity,
title = {{Rigidity of positive mass theorem with fast metric decay}},
author = {Jianchun Chu and Man-Chun Lee and Jingbo Wan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.17236},
eprint = {2607.17236},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.17236},
}
RIS
TY - UNPB
TI - Rigidity of positive mass theorem with fast metric decay
AU - Jianchun Chu
AU - Man-Chun Lee
AU - Jingbo Wan
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.17236
UR - https://arxiv.org/abs/2607.17236
AB - In this work, we consider metrics on Euclidean space with nonnegative scalar curvature and rapid decay at infinity. We show that, in dimensions four and higher, any such metric is necessarily flat if its decay rate exceeds that of the Schwarzschild metric. This complements recent works by Mazurowski-Yao and You-Zhang, thereby establishing Gromov's conjecture on the rigidity of the positive mass theorem under fast metric decay in all dimensions. Our method also extend naturally to weakly asymptotically flat manifolds.
ER -