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arXiv · 2604.08473

A dimension descent scheme for the positive mass theorem in arbitrary dimension

S. Brendle·Y. Wang
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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.

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S. Brendle, Y. Wang. 2026-04-09. A dimension descent scheme for the positive mass theorem in arbitrary dimension. https://arxiv.org/abs/2604.08473

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