Related papers: A note on the positive mass theorem with boundary
We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to…
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…
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.
In this paper, we explore positivity bounds for the effective field theory~(EFT) of a single weakly coupled massive vector field. The presence of both mass and spin makes the crossing properties of the amplitudes vastly complicated -- we…
In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted…
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…
We investigate numerically how accurately one could constrain the strengths of different short-range contributions to neutrino-less double beta decay in effective field theory. Depending on the outcome of near-future experiments yielding…
In this talk I will focus on theoretical issues related to high precision determinations of the top mass. Several mass definitions are reviewed and their respective advantages and disadvantages are discussed. Precision determinations of the…
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 Witten, we prove the following theorem: For…
We establish the charged Penrose inequality for time symmetric initial data sets having an outermost minimal surface boundary and finitely many asymptotically cylindrical ends, with an appropriate rigidity statement. This is accomplished by…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
The positive mass theorem in higher dimensions is proved using causality arguments inspired by those of Penrose, Sorkin and Woolgar in 3+1 dimensions.
We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W^{2, n/2}_{\mathrm{loc}}(M)$. We argue that this is the largest class of metrics with scalar curvature a positive a.c. measure for which the positive…
We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still…
A range of experimental results point to the existence of a massive neutrino. The recent high precision measurements of the cosmic microwave background and the large scale surveys of galaxies can be used to place an upper bound on this…
A new inequality for a nonlinear surface layer integral is proved for minimizers of causal variational principles. This inequality is applied to obtain a new proof of the positive mass theorem with volume constraint. Next, a positive mass…
A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that positive energy-density focuses null…
In this Note we show that the notion of a basis of a finite-dimensional vector space could be introduced by an argument much weaker than Gauss' reduction method. Our aim is to give a short proof of a simply formulated lemma, which in fact…
We give, via elementary methods, explicit formulas for the ADM mass which allow us to conclude the positive mass theorem and Penrose inequality for a class of graphical manifolds which includes, for instance, that ones with flat normal…