相关论文: Jang's equation and its applications to marginally…

Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…

We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This,…

The aim of this work is to present an initial data version of Hawking's theorem on the topology of back hole spacetimes in the context of manifolds with boundary. More precisely, we generalize the results of G. J. Galloway and R. Schoen…

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally…

Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…

Molecular magneto-optical traps (MOTs) typically capture orders of magnitude fewer particles than their atomic counterparts due in part to their significantly lower capture velocities. Here, we employ a Stochastic Schr\"odinger Equation…

We present a quantum theory of a magneto-optical trap (MOT) from first principles based on the quantum kinetic equation for the atomic density matrix with taking into account the recoil effects caused by the interaction of atoms with the…

We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions. More precisely, we prove a scale-invariant semi-global…

In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped…

We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…

Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.

Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped…

This paper studies the multi-marginal Monge problem in the setting of compact metric spaces proving existence and uniqueness of solutions when the cost function is Lipschitz. We apply the results obtained to solve an optics problem…

The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…

The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of…

The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Amp\`ere type known as generated Jacobian equations. These equations, whose general existence theory has been recently…

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer…

We discuss recent progress in understanding the effects of certain trapping geometries on cut-off resolvent estimates, and thus on the qualititative behavior of linear evolution equations. We focus on trapping that is unstable, so that…

In this paper, we explore the formation of the marginally trapped and marginally anti-trapped surfaces that arise from the evolution of homogeneous dust in D-dimensions with and without the cosmological constant, this is seen through the…

We examine some common features of minimal surfaces, nonzero constant mean curvature surfaces and marginally outer trapped surfaces, concerning their stability and rigidity, and consider some applications to Riemannian geometry and general…