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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.

Keywords

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}
}
R2 v1 2026-07-01T08:06:31.870Z