Related papers: Geometric Asymptotics and Beyond
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
A semi-global isometric embedding of abstract surfaces with Gaussian curvature changing signs of any finite order is obtained through solving the Darboux equation.
We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries…
We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.
We consider here the dynamics of some homogeneous and isotropic cosmological models with $N$ interacting classical scalar fields non-minimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for…
We analyze the radiative aspects of nonsymmetric gravity theory to show that, in contrast to General Relativity, its nonstationary solutions cannot simultaneously exhibit acceptable asymptotic behavior at both future and past null infinity:…
The gravitational field exterior respectively interior to a spherically symmetric, isolated body made of perfect fluid is examined within the quasi-metric framework (QMF). It is required that the gravitational field is "metrically static",…
We argue that, when a theory of gravity and matter is endowed with (classical) conformal symmetry, the fine tuning required to obtain the cosmological constant at its observed value can be significantly reduced. Once tuned, the cosmological…
We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a…
We show that every globally asymptotically stable system with a twice continuously differentiable vector field admits a local polynomial Lyapunov function on an arbitrary bounded neighborhood of the origin.
In this paper, we extend the definition of qx-asymptotic function, for extended real-valued function that define on an infinite dimensional topological normed space without lower semicontinuity or quasi-convexity condition. As the main…
A nonstationary spherically symmetric problem for conformal geometrodynamics equations is considered and general exact solutions in quadratures are obtained. Involvement of Weyl degrees of freedom allows us to consider the problem with…
We describe a rigorous construction, using matched asymptotic expansions, which establishes under very general conditions that local terrestrial and solar-system experiments will measure the effects of varying `constants' of Nature…
The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This…
Suppose that the origin is globally asymptotically stable under a set of continuous vector fields on Euclidean space and suppose that all those vector fields come equipped with -- possibly different -- convex Lyapunov functions. We show…
We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.
In this brief review, we report on the status of asymptotic symmetries of gravity corresponding to the class of metrices named asymptotically flat spacetimes in higher (d > 4) dimensions. We discuss the consequences of these symmetries both…
In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker's type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
In this paper, we establish the existence of large solutions of Hessian equations and obtain a new boundary asymptotic behavior of solutions.