Francesca Oronzio

Weighted decomposition of vector fields, $X$-ADM mass, and higher-dimensional mass-charge inequalities

We study the $X$-ADM mass on complete, one-ended asymptotically flat Riemannian manifolds without boundary in arbitrary dimension $n\geqslant 3$. Starting from a weighted gradient--divergence-free decomposition of the vector field $X$, we construct a conformal metric whose scalar curvature is governed by the critical m...