Related papers: Comments on Penrose inequality with angular moment…
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincar\'e type inequality. We apply such inequality to higher-order mean curvature of…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent…
If two particles collide inside the ergosphere, the energy in the centre of mass frame can be made unbound provided at least one of particles has a large negative angular momentum (A. A. Grib and Yu. V. Pavlov, Europhys. Lett. 101, 20004…
On an asymptotically flat manifold $M^n$ with nonnegative scalar curvature, with outer minimizing boundary $\Sigma$, we prove a Penrose-like inequality in dimensions $ n < 8$, under suitable assumptions on the mean curvature and the scalar…
We carry out model independent analyses for global structures of spherically symmetric regular black holes that evaporate and approach the extremal state spending infinite periods of time due to Hawking radiation. We assume the radius of…
We introduce a symmetric (log-)epiperimetric inequality, generalizing the standard epiperimetric inequality, and we show that it implies a growth-decay for the associated energy: as the radius increases energy decays while negative and…
In this paper we prove a rigidity result for the equality case of the Penrose inequality on $3$-dimensional asymptotically flat manifolds with nonnegative scalar curvature and corners. Our result also has deep connections with the equality…
Alternating minimization (AM) procedures are practically efficient in many applications for solving convex and non-convex optimization problems. On the other hand, Nesterov's accelerated gradient is theoretically optimal first-order method…
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…
We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality $8\pi|J|<A$ holds, where $J$ is the angular momentum and $A$ the horizon area of the black hole.
In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type…
We describe a nonsmooth notion of globally hyperbolic, regular length metric spacetimes $(\mathrm{M},l)$. It is based on ideas of Kunzinger-S\"amann, but does not require Lipschitz continuity of causal curves. We study geodesics on…
The uncertainty relations for angle and angular momentum are revisited. We use the exponential of the angle instead of the angle itself and adopt dispersion as a natural measure of resolution. We find states that minimize the uncertainty…
Covariant conserved 2-form currents for linearised gravity are constructed by contracting the linearised curvature with conformal Killing-Yano tensors. The corresponding conserved charges were originally introduced by Penrose and have…
We investigate the compact submanifolds in Riemannian space forms of nonnegative sectional curvature that satisfy a lower bound on the Ricci curvature, that bound depending solely on the length of the mean curvature vector of the immersion.…
We consider the unit speed parametrization of the horocycle flow on infinite Abelian covers of compact surfaces of negative curvature. We prove an asymptotic result for the ergodic integrals of sufficiently regular functions. In the case of…
In this paper, the connection between the Lorentz-covariant counterterms that regularize the four-dimensional AdS gravity action and topological invariants is explored. It is shown that demanding the spacetime to have a negative constant…
Using harmonic mean curvature flow, we establish a sharp Minkowski type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard 3-manifolds. This inequality also improves the known estimates for total…
The past lightcone of an observer in a cosmological spacetime is the unique geometric structure directly linked to observations. After general properties of the Hawking energy along slices of the past lightcone have previously been studied,…