Related papers: Comments on Penrose inequality with angular moment…
We obtain an energy inequality on null surfaces $u=const$ in the Bondi-Sachs formalism. We show that for a sufficiently regular event horizon $H$ there is an affine radial coordinate which is constant on $H$. Then the energy inequality can…
We prove capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boundary. We then give the analogous of P\"olia-Szeg\"o,…
In this paper, we consider conformal metrics on a unit 4-disc with an asymptotically hyperbolic end and possible isolated conic singularities. We define a mass term of the AH end. If the $\sigma_{2}$ curvature has lower bound…
For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the…
We provide a new proof of the Riemannian Penrose inequality for time-symmetric asymptotically flat initial data with a single black-hole horizon. The proof proceeds through a newly established monotonicity formula holding along the level…
We show that the area-angular momentum inequality A\geq 8\pi|J| holds for axially symmetric closed outermost stably marginally trapped surfaces. These are horizon sections (in particular, apparent horizons) contained in otherwise generic…
We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…
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…
In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^{6}-$norm bound for the difference between general data and…
Penrose's weak cosmic censorship conjecture asserts that spacetime singularities produced by gravitational collapse are generically hidden behind event horizons, thus preventing them from causally influencing distant observers and…
We extend the analysis by Esedo\={g}lu and Otto (2015) of thresholding energies for the celebrated multiphase Bence-Merriman-Osher algorithm for computing mean curvature flow of interfacial networks, to the case of differing space-dependent…
The semicontinuity phenomenon of the ADM mass under pointed (i.e., local) convergence of asymptotically flat metrics is of interest because of its connections to nonnegative scalar curvature, the positive mass theorem, and Bartnik's…
Riemannian Penrose Inequalities are precise geometric statements that imply that the total mass of a zero second fundamental form slice of a spacetime is at least the mass contributed by the black holes, assuming that the spacetime has…
We study time symmetric initial data for asymptotically AdS spacetimes with conformal boundary containing a spatial circle. Such $d$-dimensional initial data sets can contain $(d-2)$-dimensional minimal surfaces if the circle is…
The Penrose strong cosmic censorship conjecture asserts that Cauchy horizons inside dynamically formed black holes are unstable to remnant matter fields that fall into the black holes. The physical importance of this conjecture stems from…
On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation.…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
We prove an inequality between horizon area and angular momentum for a class of axially symmetric black holes. This class includes initial conditions with an isometry which leaves fixed a two-surface. These initial conditions have been…
We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As…
For a stable marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant $\Lambda > 0$ and with matter satisfying the dominant energy condition, we prove that the area $A$ and the angular momentum…