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

TL;DR

This paper proves the Riemannian positive mass theorem up to dimension 19 using advanced geometric techniques, and also explores the Geroch conjecture up to dimension 12.

Contribution

It extends the positive mass theorem proof to higher dimensions and applies similar methods to the Geroch conjecture, advancing geometric analysis.

Findings

Positive mass theorem proven up to dimension 19

Geroch conjecture investigated up to dimension 12

Utilizes torical symmetrization and singularity blow-up techniques

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 $12$.