A Non-spin Method to the Positive Weighted Mass Theorem for Weighted Manifolds

Abstract

In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of P-scalar curvature, we are able to prove the positive weighted mass theorem for weighted manifolds, which generalizes the result of Baldauf–Ozuch (Commun Math Phys 394(3):1153–1172, 2022) to non-spin manifolds.