A Conformal Positive Mass Theorem with Noncompact Boundary
Differential Geometry
2025-12-04 v1
Abstract
We obtain an integral inequality for asymptotically linear harmonic functions on asymptotically flat 3-manifolds with noncompact boundary, which implies positivity of a convex combination of ADM masses of two conformally related metrics under a positivity condition on a corresponding convex combination of their scalar curvatures and boundary mean curvatures. This generalizes a result of Batista and Lopes de Lima, under conditions that do not assume positivity of scalar curvature.
Cite
@article{arxiv.2512.03212,
title = {A Conformal Positive Mass Theorem with Noncompact Boundary},
author = {Alex Freire and Mohammad Tariquel Islam},
journal= {arXiv preprint arXiv:2512.03212},
year = {2025}
}