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

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 $12$.