A proof for the Riemannian positive mass theorem up to dimension 19

Yuchen Bi; Tianze Hao; Shihang He; Yuguang Shi; Jintian Zhu

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arXiv · 2603.02769

A proof for the Riemannian positive mass theorem up to dimension 19

Yuchen Bi·Tianze Hao·Shihang He·Yuguang Shi·Jintian Zhu

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Abstract

In this paper, we prove the Riemannian positive mass theorem up to dimension $19$, building on a combination of torical symmetrization and the singularity blow-up technique developed in [HSY26], together with the generic regularity theory for area-minimizing hypersurfaces established in [CMS23, CMSW25]. Similar ideas are also employed to investigate the Geroch conjecture up to dimension $12$.

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Yuchen Bi, Tianze Hao, Shihang He, Yuguang Shi, Jintian Zhu. 2026-03-03. A proof for the Riemannian positive mass theorem up to dimension 19. https://arxiv.org/abs/2603.02769

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