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

Published 3 Mar 2026 in math.DG | (2603.02769v1)

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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