A Conformal Positive Mass Theorem with Noncompact Boundary

2025/12/02 by Freire, Alex, Islam, Mohammad Tariquel
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.03212

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.

Citations

• A harmonic level set proof of a positive mass theorem
• Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds
• The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary
• Some Conformal Positive Mass Theorems
• A positive mass theorem for asymptotically flat manifolds with a non-compact boundary
• The mass of an asymptotically flat manifold

Related

• A harmonic level set proof of a positive mass theorem
• Conformal positive mass theorems
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature
• Curvature Estimates and the Positive Mass Theorem
• Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds