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

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

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

Differential Geometry 2026-03-30 v2

Authors: Yuchen Bi , Tianze Hao , Shihang He , Yuguang Shi , Jintian Zhu

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 $12$ .

Keywords

Riemannian positive mass theorem torical symmetrization singularity blow-up generic regularity area-minimizing hypersurfaces Geroch conjecture

Cite

@article{arxiv.2603.02769,
  title  = {A proof for the Riemannian positive mass theorem up to dimension 19},
  author = {Yuchen Bi and Tianze Hao and Shihang He and Yuguang Shi and Jintian Zhu},
  journal= {arXiv preprint arXiv:2603.02769},
  year   = {2026}
}

Comments

38 pages, no figure, some typos corrected

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

Abstract

Keywords

Cite

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