arXiv research

Study proves inequalities for mass-capacity on curved spaces.

The article proves charged quasi-local Penrose inequalities for compact manifolds with boundary.

New mass definition linked to ADM mass for general metrics.

Proves Riemannian Penrose Inequality for specific manifolds.

Study on charged parallel spinors and mass-charge inequalities.

New inequality on sphere generalizes circle inequality.

In this paper lower bounds are obtained for quasi-local masses in terms of charge, angular momentum, and horizon area. In particular we treat three quasi-local masses based on a Hamiltonian approach, namely the Brown-York, Liu-Yau, and Wang-Yau masses. The geometric inequalities are motivated by analogous results for t…

The paper consists of two parts. In the first part, by using the Gauss-Bonnet curvature, which is a natural generalization of the scalar curvature, we introduce a higher order mass, the Gauss-Bonnet-Chern mass $m^{\H}_k$, for asymptotically hyperbolic manifolds and show that it is a geometric invariant. Moreover, we pr…

Study shows mass-capacity inequality for specific geometric manifolds.

The study examines mass drop and multiplicity in mean curvature flow.

New geometric inequality for mass from immersed submanifolds.

New methods using spacetime harmonic functions solve geometric inequalities.

New mass inequalities and proofs for causal variational principles.

In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, Pólya-Szegö and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is char…

In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -6 and negative mass when the genus of the conformal boundary at infinity is positive. Using inverse mean curvature flow, we prove a Penrose inequality for these negative mass metrics. The motivation comes fro…

The paper establishes inequalities for $p$-capacitary functions in flat half-spaces.

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 bundle.

New method improves missing mass concentration bounds.

The paper proves a new inequality linking mass and volume in 3D space.

The paper studies nonlinear mass concepts in 3-manifolds with nonnegative scalar curvature.

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …

Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for missing mass and improve the results of Berend and Kontorovich (2013) and Yari Saeed…

The study proves stability of the positive mass theorem for Kähler manifolds.

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,θ)$, we study the existence of a contact structure conformal to $θ$ for which the logarithmic Hardy-Littlewood-Sobolev (LHLS) inequality holds. Our approach closely follows \cite{Ok1} in the Riemannian setting. For this purpose, we introduce the notion …

Paper proves flat 3-manifolds with positive mass have unique isoperimetric surfaces.

Study connects isoperimetric sets, mass concepts, and nonnegative scalar curvature.

The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.

Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.

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 by the standard Green's function for the Laplacian operator. As an application,…

New mass and staticity concepts derived from weighted curvature maps.

The paper extends the spacetime positive mass theorem to multiple time dimensions.

Generalizes inequality for complete manifolds involving homology classes.

We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\geq 3$ an optimal Penrose inequality for certain graphs in hyperbolic space $\mathbb H^{n+1}$ whose boundary…

Sharp inequalities in nonnegative Ricci curvature spaces using mass transport.

The positive mass theorem is one of the fundamental results in general relativity. It states that, assuming the dominant energy condition, the total mass of an asymptotically flat spacetime is non-negative. The Penrose inequality provides a lower bound on mass by the area of the black hole and is closely related to the…

We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like deviation bounds with sublinear exponents in deviation size for missing mass, but …

We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus provin…

Paper proves stronger Penrose inequality with matter density.

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which p…

In this paper, we prove a positive mass theorem and Penrose-type inequality of the Gauss-Bonnet-Chern mass $m_2$ for the graphic manifold with flat normal bundle.

Derives monotonic quantities for $p$-harmonic functions on manifolds.

For a closed surface M with metric g, the Robin mass m(p) at the point p is the value of the Green function G(p,q) at p=q after the logarithmic singularity has been removed. The Laplacian-mass is the average value of the Robin mass, minus the value of the Robin mass for the round sphere of the same area. The Laplacian-…

The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.

The paper proves a new inequality for 3-manifolds with noncompact boundaries.

Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.

Establishes inequality for multiple black holes, proving mass lower bound.

We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…

In this paper we show positive mass theorems and Penrose type inequalities for the Gauss-Bonnet-Chern mass, which was introduced recently in \cite{GWW}, for asymptotically flat CF manifolds and its rigidity.