• Corpus ID: 237605384

On a spacetime positive mass theorem with corners

  title={On a spacetime positive mass theorem with corners},
  author={Tin-Yau Tsang},
In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump conditions on the metric and second fundamental form which are sufficient for the positivity of the total spacetime mass. Our method extends that of [30] to the singular case (which we refer to as initial data sets with corners) using some ideas from [31]. As such we give an integral lower bound on the… 

Dihedral rigidity for cubic initial data sets

In this paper we pose and prove a spacetime version of Gromov’s dihedral rigidity theorem ([17],[24],[25]) for cubes when the dimension is 3 by studying the level sets of spacetime harmonic functions

Rigid comparison geometry for Riemannian bands and open incomplete manifolds

. Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either

Nonexistence of DEC spin fill-ins

  • S. Raulot
  • Mathematics
    Comptes Rendus. Mathématique
  • 2022
. In this note, we show that a closed spin Riemannian manifold does not admit a spin fill-in satisfying the dominant energy condition (DEC) if a certain generalized mean curvature function is



The spacetime positive mass theorem in dimensions less than eight

We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM

Spacetime Harmonic Functions and Applications to Mass

In the pioneering work of Stern [73], level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing

Spacetime Positive Mass Theorems for Initial Data Sets with Non-Compact Boundary

In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under

A localized spacetime Penrose inequality and horizon detection with quasi-local mass.

Our setting is a simply connected bounded domain with a smooth connected boundary, which arises as an initial data set for the general relativistic constraint equations satisfying the dominant energy

Positivity of mass for certain spacetimes with horizons

Assuming the existence of a solution of the 3-harmonic equation Del i( mod Del rho mod 3 Del i rho )=0 on a spacelike 3-manifold Sigma with boundary K(assume that the solution has no critical points

Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations

We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in

On the proof of the positive mass conjecture in general relativity

LetM be a space-time whose local mass density is non-negative everywhere. Then we prove that the total mass ofM as viewed from spatial infinity (the ADM mass) must be positive unlessM is the flat

Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space

We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown--York quasi-local mass as it possesses positivity and rigidity properties, and therefore the

Total mean curvature of the boundary and nonnegative scalar curvature fill-ins

Abstract In the first part of this paper, we prove the extensibility of an arbitrary boundary metric to a positive scalar curvature (PSC) metric inside for a compact manifold with boundary,

Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and with nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and