A dimension descent scheme for the positive mass theorem in arbitrary dimension
Differential Geometry
2026-04-21 v2
Abstract
We describe how the Schoen-Yau proof of the positive mass theorem can be extended to arbitrary dimensions. To overcome the problem of singularities, we propose a new inductive scheme. To carry out the inductive step, we use a combination of several techniques, including the shielding principle of Lesourd-Unger-Yau, as well as a conformal blow-up argument in the spirit of Bi-Hao-He-Shi-Zhu. Our arguments also rely on the Cheeger-Naber bound for the Minkowski dimension of the singular set.
Cite
@article{arxiv.2604.08473,
title = {A dimension descent scheme for the positive mass theorem in arbitrary dimension},
author = {S. Brendle and Y. Wang},
journal= {arXiv preprint arXiv:2604.08473},
year = {2026}
}
Comments
minor improvements in exposition