A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Sharp bounds for charged Hawking mass in electrostatic space-times.
Stability of positive mass theorem proven under Ricci curvature bounds.
Establishes inequality for multiple black holes, proving mass lower bound.
Rigidity results for Hawking mass in curved spaces with bounds on Bartnik capacity.
The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein-Maxwell equations, wh…
Constructs fill-ins with scalar curvature lower bounds for geometric applications.
The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy condition without a cosmological constant. There is a natural analogue of the Bartnik…
Researchers prove positive mass theorem for manifolds with arbitrary ends.
Positive mass theorem for asymptotically flat manifolds with non-negative distributional scalar curvature
Study proves inequalities for mass-capacity on curved spaces.
In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with …
Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed Cheeger--Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. I…
Defines mass for non-smooth hyperbolic spaces using a modified flow.
The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a …
In this paper, we obtain lower bounds for the Brown-York quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions for the existence of horizons for a certain class of compact manifolds with boundary and some asymptotically flat…
Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
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…
New bounds on Bartnik mass for surfaces with non-negative first eigenvalue.
The Positive Mass Theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass. The Riemannian Penrose inequality provides a sharp lower bound for the mass when black holes are present. More precisely, this lower bound is given in terms of the area of an outermost min…
Study shows rigidity of polyhedrons in hyperbolic spaces.
The paper develops new methods to study sharp isoperimetric properties on complex spaces.
New examples of manifolds with lower scalar curvature bounds and submanifold collapse.
The paper proves mass nonnegativity for certain asymptotically locally flat manifolds.
New formulas for hyperbolic mass using horospheres.
3D metrics get scalar curvature bounds via IMCF.
Paper bounds total geodesic curvature using boundary data in hyperbolic gravity.
The Riemannian hemisphere has a lower bound for its mass.
Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standard sphere. The Hawking mass gives a well-known lower bound, and an upper bound is obtained by estimating the mass of a static vacuum extensi…
Positive mass theorem for tori with scalar curvature bounds.
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes.…
Rigidity results for initial data sets related to the positive mass theorem.
We give some lower estimates of the ADM mass of an asymptotically flat (AF) Riemannian manifold without assuming that the scalar curvature of the manifold is nonnegative. Some sufficient conditions for an AF manifold to have nonnegative ADM mass are obtained. We also give some lower estimates of the Brown-York mass of …
Sharp mass bounds for ALE and ALF toric 4-manifolds.
The paper proves a new inequality linking mass and volume in 3D space.
The study proves stability of the positive mass theorem for Kähler manifolds.
We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over . 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…
Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular this result does not require the res…
The paper calculates mass and volume of Einstein metrics in four dimensions.
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 …
New proof of Positive Mass Theorem using Green's function and monotonicity formula.
The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We develop a theory of such "zero area singularities" in Riemannian manifolds, general…
Compact gravity models yield tiny spin-two field masses.
In this paper we characterize the intrinsic geometry of apparent horizons (outermost marginally outer trapped surfaces) in asymptotically flat spacetimes; that is, the Riemannian metrics on the two sphere which can arise. Furthermore we determine the minimal ADM mass of a spacetime containing such an apparent horizon. …
The paper proves a spacetime positive mass theorem for singular initial data sets.
The paper studies Kähler metrics from finite Monge-Ampère mass exhaustion functions.
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…
Study rigidity of minimal disks in specific 3-manifolds.
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.