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

We prove the Riemannian positive mass theorem up to dimension 19, building on a combination of torical symmetrization and the singularity blow-up technique, together with the generic regularity theory for area-minimizing hypersurfaces developed by Chodosh, Mantoulidis, Schulze and Wang. This is a joint work with Yuchen Bi, Tianze Hao, Yuguang Shi and Jintian Zhu.