Related papers: A positive mass theorem for low-regularity metrics

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give…

We formulate and prove a positive mass theorem for n-dimensional spin manifolds whose metrics have only the Sobolev regularity $C^0 \cap W^{1,n}$. At this level of regularity, the curvature of the metric is defined in the distributional…

We prove that the positive mass theorem applies to Lipschitz metrics as long as the singular set is low-dimensional, with no other conditions on the singular set. More precisely, let $g$ be an asymptotically flat Lipschitz metric on a…

This paper deals with quasi-local isoperimetric versions of the positive mass theorem on $3$-manifolds endowed with continuous complete metrics having nonnegative scalar curvature in a suitable weak sense. As a corollary, we derive…

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…

We prove a Riemannian positive mass theorem for manifolds with a single asymptotically flat end, but otherwise arbitrary other ends, which can be incomplete and contain negative scalar curvature. The incompleteness and negativity is…

The Positive Mass Conjecture states that any complete asymptotically flat manifold of nonnnegative scalar curvature has nonnegative mass. Moreover, the equality case of the Positive Mass Conjecture states that in the above situation, if the…

This article establishes a low-regularity Riemannian positive mass theorem for non-spin manifolds whose metrics are only $C^0 \cap W_{\mathrm{loc}}^{1,n}$ and smooth outside a compact set. The main theorem asserts that asymptotically flat…

Motivated by the recent progress on positive mass theorem for asymptotically flat manifolds with arbitrary ends and the Gromov's definition of scalar curvature lower bound for continuous metrics, we start a program on the positive mass…

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the…

We define the "sum of squares of the wavelengths" of a Riemannian surface (M,g) to be the regularized trace of the inverse of the Laplacian. We normalize by scaling and adding a constant, to obtain a "mass", which is scale invariant and…

We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green's function. The theorem also holds if the conformal Green's function is replaced…

The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3-manifold with non-negative scalar curvature which has zero total mass is isometric to (R^3, delta_{ij}). In this paper, we quantify this statement using…

On a compact three-dimensional Riemannian manifold with boundary, we prove the compactness of the full set of conformal metrics with positive constant scalar curvature and constant mean curvature on the boundary. This involves a blow-up…

We show the contractibility of spaces of invariant Riemannian metrics of positive scalar curvature on compact connected manifolds of dimension at least two, with and without boundary and equipped with compact Lie group actions. On manifolds…

The positive mass theorem states that the total mass of a complete asymptotically flat manifold with non-negative scalar curvature is non-negative; moreover, the total mass equals zero if and only if the manifold is isometric to the…

Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over…

W. Simon proved a conformal positive mass theorem, which was used to prove uniqueness of black holes later. In this note, we will generalize Simon's conformal positive mass theorem in two directions. First we will consider spacetime version…

Built on a recent work of Almaraz, Barbosa, de Lima on positive mass theorems on asymptotically flat manifods with a noncompact boundary, we apply free boundary minimal surface techniques to prove their positive mass theorem and study the…

We establish Gromov-Hausdorff stability of the Riemannian positive mass theorem under the assumption of a Ricci curvature lower bound. More precisely, consider a class of orientable complete uniformly asymptotically flat Riemannian…