arXiv research

Study confirms conjecture on Hermitian manifolds with bounded mass.

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…

Rigidity results for Hawking mass in curved spaces with bounds on Bartnik capacity.

Study volumes of Bott-Chern classes on complex manifolds.

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

In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus on the rigidity property: for a surface in the Minkowski spacetime, one expects t…

Study proves positivity of quasi-local masses in general relativity using spinors.

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…

Sharp bounds for charged Hawking mass in electrostatic space-times.

The paper develops new methods to study sharp isoperimetric properties on complex spaces.

Upper bounds on Bartnik mass for non-negatively curved spheres.

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 twenty years ago \cite{SchoenYau79b,Witten81}, is a remarkable testament to this f…

Stability of positive mass theorem proven under Ricci curvature bounds.

Sharp bounds for anisotropic p-capacity of Euclidean compact sets derived using flow methods.

New method improves missing mass concentration bounds.

Positive mass theorem for asymptotically flat manifolds with non-negative distributional scalar curvature

Positive mass theorem for tori with scalar curvature bounds.

The paper proves mass nonnegativity for certain asymptotically locally flat manifolds.

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…

Study proves inequalities for mass-capacity on curved spaces.

The paper extends spin geometry to weighted manifolds and defines a new mass for Ricci flow.

Sharp mass bounds for ALE and ALF toric 4-manifolds.

Defines mass for non-smooth hyperbolic spaces using a modified flow.

A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem

New bounds on Bartnik mass for surfaces with non-negative first eigenvalue.

Bartnik mass is positive and non-decreasing for black holes

We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity. Moreover, the new quasi-local energy has the positivity property.

We bound the locations of outermost minimal surfaces in geometrostatic manifolds whose ADM mass is small relative to the separation between the black holes and prove the Intrinsic Flat Stability of the Positive Mass Theorem in this setting.

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

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…

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…

Researchers prove positive mass theorem for manifolds with arbitrary ends.

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

The paper explores stable surfaces in Einstein-Maxwell theory, proving mass bounds and nonexistence results.

Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass. We also obtain estimates of the Bartnik mass of such surfaces, without assumptions on the integral of the squared mea…

This paper surveys recent progress on issues related to the Bartnik quasi-local mass $m_B$. In addition, we formulate a number of new problems and conjectures regarding foundational properties of the mass $m_B$. This work is dedicated with pleasure to Robert Bartnik in honor of his 60th birthday.

Improved mass-capacity bounds for specific 3D manifolds.

Paper defines Bartnik mass for hyperbolic extensions and proves staticity.

Continuous metrics on R^3 with specific properties have non-negative harmonic mass.

Estimates mass of static vacuum metrics with small Bartnik data.

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 spinors and prove that if a complete, asymptotically flat manifold with non-negative…

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

The mass of asymptotically hyperbolic ends and manifolds is analyzed.

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…

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…

Paper bounds total geodesic curvature using boundary data in hyperbolic gravity.

Unified definition of mass aspect function for weakly regular hyperbolic manifolds.

The study extends conserved quantities theory to non-compact boundary initial data sets.