Related papers: Geometric Asymptotics and Beyond

We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…

This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…

Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…

We contribute to the arithmetic/topology dictionary by relating asymptotic point counts and arithmetic statistics over finite fields to homological stability and representation stability over $\Cb$ in the example of configuration spaces of…

We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation…

A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…

This article establishes several necessary and sufficient criteria on asymptotic stability and mean ergodicity in various types of topologies for Feller processes taking values in Polish spaces. In particular, asymptotic stability and mean…

This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.

We discuss the asymptotic form of the static axially symmetric, globally regular and black hole solutions, obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory.

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…

We survey recent results about asymptotic functions of groups, obtained by the authors in collaboration with J.-C.Birget, V. Guba and E. Rips. We also discuss methods used in the proofs of these results.

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…

Bimetric gravity can reproduce the accelerated expansion of the Universe, without a cosmological constant. However, the stability of these solutions to linear perturbations has been questioned, suggesting exponential growth of structure in…

Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.

The asymptotic Dirichlet problem for harmonic maps from the hyperbolic plane into conformally compact Einstein manifolds is used to give a holographic characterization of conformal geodesics on the boundary at infinity, in a way deeply…

The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.

We consider polynomial differential equations and make a number of contributions to the questions of (i) complexity of deciding stability, (ii) existence of polynomial Lyapunov functions, and (iii) existence of sum of squares (sos) Lyapunov…

The feedback exponential stabilization to trajectories for semilinear parabolic equations in a given bounded domain is addressed. The controls take values in a finite-dimensional space and are supported in a small region. Both internal and…

We conjecture that meanders are governed by the gravitational version of a c=-4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent \alpha=\sqrt{29}(\sqrt{29}+\sqrt{5})/12, and the…