Introduce new boundary mass for asymptotically flat half-manifolds
problem Define boundary mass for asymptotically flat half-manifolds
method Introduce new boundary mass
result Define boundary mass for asymptotically flat half-manifolds
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48 results for “boundary mass”
Study the mass of flat 3-manifolds with boundary using specific methods.
problem Calculate the mass of asymptotically flat 3-manifolds with boundary.
method Use the method of Bray-Kazaras-Khuri-Stern to derive a mass formula.
result Derive sufficient conditions for the positivity of the mass.
We study Hawking mass and the Huisken's isoperimetric mass evaluated on surfaces with boundary. The convergence to an ADM mass defined on asymptotically flat manifold with a non-compact boundary are proved.
New theorem for spacetime mass in noncompact regions.
problem Mass in noncompact spacetime regions.
method Developed mass type invariant and boundary conditions; proof based on spinors.
result Proved positive mass theorem for noncompact boundaries.
Study on ALH manifolds with boundary, showing surjectivity of scalar curvature map and mass rigidity.
problem Characterizing ALH manifolds with boundary and their mass.
method Scalar curvature deformation analysis and mass rigidity study.
result ALH manifolds that minimize mass integrals are characterized.
Proves positive mass theorems for specific types of curved spaces.
problem Analyzing mass in curved spaces with boundaries.
method Proves positive mass theorems for specific types of curved spaces with boundaries.
result Establishes conditions under which mass is positive in these spaces.
Explains how to prove positive mass theorem with boundary in dimensions less than 8.
problem Proving the positive mass theorem with boundary conditions.
method Uses established results to prove various versions of the theorem.
result Various versions of the positive mass theorem are proven for initial data sets with boundary in dimensions less than 8.
Paper proves rigidity of 3-manifolds with boundary using modified Hawking mass.
problem Rigidity of 3-manifolds with boundary under specific geometric conditions.
method Area estimates for free boundary strictly stable two-disks, modified Hawking mass analysis.
result 3-manifolds with boundary are locally isometric to half anti-de Sitter-Schwarzschild manifold.
The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
problem Connections among ADM mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
method New formulae for ADM mass via harmonic functions, monotone quantities, and geometric inequalities.
result The mass-to-capacity ratio is bounded below by 1 - sqrt(normalized Willmore functional of the boundary).
Positive mass theorem for non-smooth metrics on flat manifolds with corners.
problem Proving a positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary.
method Proves a positive mass theorem for metrics that are only continuous across a compact hypersurface.
result Obtains a positive mass theorem on manifolds with non-compact corners.
The paper proves a new inequality for 3-manifolds with noncompact boundaries.
problem Proving positivity of a convex combination of ADM masses on 3-manifolds with noncompact boundaries.
method Obtained an integral inequality for asymptotically linear harmonic functions.
result Positivity of a convex combination of ADM masses under a positivity condition on scalar curvatures and boundary mean curvatures.
We extend the idea and techniques in \cite{Miao} to study variational effect of the boundary geometry on the ADM mass of an asymptotically flat manifold. We show that, for a Lipschitz asymptotically flat metric extension of a bounded Riemannian domain with quasi-convex boundary, if the boundary mean curvature of the ex…
Built on a recent work of Almaraz, Barbosa, de Lima on positive mass theorems on asymptotically flat manifods with a noncompact boundary, we apply free boundary minimal surface techniques to prove their positive mass theorem and study the existence of positive scalar curvature metrics with mean convex boundary on a con…
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
Proves positive mass theorem for 3-manifolds with a boundary.
problem Proving the positive mass theorem for specific 3-manifolds.
method Uses harmonic level set approach.
result Validates the positive mass theorem for new class of manifolds.
Proves density and mass theorems for specific initial data sets.
problem Initial data sets with boundary in spacetime.
method Harmonic asymptotics and dominant energy condition.
result Spacetime positive mass theorem for initial data sets with apparent horizon boundary.
Proves critical points of ADM mass correspond to specific initial data sets.
problem Finding initial data sets with fixed Bartnik boundary data.
method Proves existence of critical points on a Banach manifold.
result Critical points of ADM mass correspond to initial data sets with generalized Killing vector fields.
Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitionsmath.DG
In the context of the Bartnik mass, there are two fundamentally different notions of an extension of some compact Riemannian manifold with boundary. In one case, the extension is taken to be a manifold without boundary in which embeds isometrically, and in the other case the extension is taken to be a m…
We define a mass-type invariant for asymptotically hyperbolic manifolds with a noncompact boundary which are modelled at infinity on the hyperbolic half-space and prove a sharp positive mass inequality in the spin case under suitable dominant energy conditions. As an application we show that any such manifold which is …
The mass of asymptotically hyperbolic ends and manifolds is analyzed.
problem Analyzing the mass of asymptotically hyperbolic ends and manifolds.
method Using Riemannian spin manifolds, scalar curvature, and mean curvature.
result The mass of an asymptotically hyperbolic end is timelike future-directed or zero.
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…
The paper solves a partial Plateau problem using -mass.
problem Finding a surface of least area with a partially specified boundary.
method Minimizing -mass over scans with boundary.
result Existence of a rectifiable minimizer for the -mass problem.
Integral currents with boundary of finite mass are integral.
problem Integral currents with boundary of finite mass are integral.
method De Giorgi's structure theorem for integer-valued functions and a cylindrical projection argument.
result Integral currents with boundary of finite mass are integral.
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 any compact manifold with boundary and nonnegative scalar curvature, if it is s…
Maps preserving mass and injective on boundary are isometries.
problem Stability of mass-preserving maps in integral current spaces.
method Proving rigidity of mass-preserving 1-Lipschitz maps.
result Maps preserving mass and injective on boundary are isometries.
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,…
In this short note, we prove positivity of Brown-York mass under quasi-positive boundary data which generalize some previous results by the authors. The corresponding rigidity result is obtained.
ADM mass, area and capacity in asymptotically flat -manifolds with nonnegative scalar curvaturemath.DG
Improved mass-capacity bounds for specific 3D manifolds.
problem Sharp mass-capacity inequality and upper bounds for 3D asymptotically flat manifolds.
method Monotonicity formulas associated with a harmonic potential.
result Improved bounds on ADM mass and capacity in terms of boundary area.
We prove the following stronger verson of the positivity of quasi-local mass stated in gr-qc/0303019: the quasi-local energy (mass) of each connected component of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the space…
Study geometric inequalities and boundary estimates for Einstein-type manifolds with boundary.
problem Investigate geometric properties of Einstein-type manifolds with boundary.
method Investigate geometric inequalities and establish boundary estimates.
result Established boundary estimates in terms of eigenvalues and Brown-York mass.
Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean spacemath.DG
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 stability of this rigidity statement can be studied. Specifically, we ask if the Brown--York mass of the boundary of some co…
For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass of the boundary and the Hawking mass of strictly minimizing hulls in the Jang graphs of the domain. Using this, we prove a quasi-local Penrose inequality that involves these…
Paper proves stability of positive mass theorem for specific types of manifolds.
problem Stability of positive mass theorem for compact graphical manifolds.
method Used Federer--Fleming flat distance and static quasi-local Brown-York energy.
result Proved stability of positive mass theorem for compact (locally) hyperbolic graphical manifolds.
Study on stellar models' topology and mass using minimal surfaces.
problem Investigating the topology and mass of static stellar models.
method Analyzing stable free boundary minimal surfaces in static perfect fluid spaces.
result Proved non-existence of stable free boundary minimal surfaces and derived upper bounds for Hawking mass.
Study mass and center of mass in flat 3-manifolds, proving existence of foliations.
problem Interplay between mass, center of mass, and isoperimetric quotients in asymptotically flat 3-manifolds.
method Adapted implicit function method and foliation techniques.
result Existence of foliations satisfying curvature conditions and unique relative isoperimetric surfaces.
Study characterizes compact Einstein-type manifolds with boundary.
problem Characterize compact Einstein-type manifolds with nonempty boundary.
method Proved a sharp boundary estimate, obtained Hawking mass bounds, and provided a topological classification for the boundary.
result Obtained a gap result for compact Einstein-type manifolds with boundary.
The paper proves a positive mass theorem for non-compact static domains in hyperbolic space.
problem Proving a positive mass theorem for non-compact static domains in hyperbolic space.
method Formulating and proving a positive mass theorem under natural dominant energy conditions, using elliptic boundary conditions on spinors.
result Retrieve a sharper version of a recent result by Souam about the rigidity of non-compact static domains.
We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric. We establish an additivity property for this supremum and exhibit rigidity for maximizers assuming the supremum is attained. When the boundary consis…
In [5] Herzlich proved a new positive mass theorem for Riemannian 3-manifolds whose mean curvature of the boundary allows some positivity. In this paper we study what happens to the limit case of the theorem when, at a point of the boundary, the smallest positive eigenvalue of the Dirac operator of the boundar…
Simple proof for sphere mass calculation.
problem Computing the ADM mass of static sphere extensions.
method Uses mass formula for static asymptotically flat manifolds.
result Validated mass formula for small spheres.
Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.
problem Proving mass-capacity inequalities for critical area-normalized capacitors.
method Analyzes asymptotically flat manifolds with boundary capacity potential satisfying an overdetermined problem.
result Improves Schwarzschild metric uniqueness and results for spin asymptotically flat spacetimes.
Study on quasi-Einstein manifolds with boundary estimates and inequalities.
problem Understanding the geometry of compact quasi-Einstein manifolds with boundary.
method Sharp boundary estimates and characterization theorems for quasi-Einstein manifolds.
result New geometric inequalities and boundary estimates for quasi-Einstein manifolds.
Solves a problem posed by Brezis and Mironescu about least mass of area-minimizing currents.
problem Least mass of area-minimizing currents with a given boundary.
method Demonstrates the value of the least mass and compares it to the infimum of areas of smoothly immersed submanifolds.
result The least mass of area-minimizing currents equals the infimum of areas of smoothly immersed submanifolds with the same boundary.
Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvaturemath.DG
On a compact Riemannian manifold with boundary having positive mean curvature, a fundamental result of Shi and Tam states that, if the manifold has nonnegative scalar curvature and if the boundary is isometric to a strictly convex hypersurface in the Euclidean space, then the total mean curvature of the boundary is no …
The article proves charged quasi-local Penrose inequalities for compact manifolds with boundary.
problem Determining if a quasi-local version of the Riemannian Penrose inequality holds for Einstein-Maxwell equations.
method Building on ideas of Lu and Miao, and the first-named author, the article proves charged quasi-local Penrose inequalities for a class of compact manifolds with boundary.
result The lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Riemannian Penrose inequality for a specific reference manifold.
Positive mass theorem for tori with scalar curvature bounds.
problem Proving positivity of static quasi-local mass for tori.
method Generalization of Shi-Tam result to 2-tori with specific curvature and scalar curvature bounds.
result Total weighted mean curvature of 2-tori is not greater than that of an isometric embedding into the Kottler manifold.
Mass in relativity linked to polyhedra geometry.
problem Understanding ADM mass in general relativity.
method Relating ADM mass to the total mean curvature and defect of dihedral angles of Riemannian polyhedra.
result Expressed -dimensional mass as an integral of geometric quantities.
The paper explores stable surfaces in Einstein-Maxwell theory, proving mass bounds and nonexistence results.
problem Exploring stable surfaces in static Einstein-Maxwell space-time.
method Using mean-stable surfaces theory to prove properties of lapse functions and mass bounds.
result Proves ADM mass is bounded by Hawking quasi-local mass.