Related papers: The Urysohn sphere is oscillation stable
We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull-Strominger system is recasted using non-Hermitian…
A mathematical model of the evolution of spherical perturbations in a cosmological ideal scalar-charged fluid with scalar Higgs interaction is constructed. A closed mathematical model of linear spherical perturbations in a cosmological…
An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt…
Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic…
We establish universality and ultra-homogeneity of $(\mathcal{U},u_\mathrm{GH})$, the collection of all compact ultrametric spaces endowed with the so-called Gromov-Hausdorff ultrametric. This result also gives rise to a novel construction…
The article treats the classical problem of stability of steady rotation of a rigid homogeneous ellipsoid on a rigid smooth plane which rotates about its vertical axis. The condition for the steady rotation is derived from the Euler-Poisson…
For any $n$-tuple $(\alpha_1,...,\alpha_n)$ of linearly independent vectors in Hilbert space $H$, we construct a unique orthonormal basis $(\epsilon_1,...,\epsilon_n)$ of $span\{\alpha_1,...,\alpha_n\}$ satisfying:…
The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterized by only one dimensionless number, the…
We study constant mean curvature Lorentzian hypersurfaces of $\mathbb{R}^{1,d+1}$ from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the…
In this paper, analytical solutions describing static and spherically symmetric sources in the decoupling limit of massive gravity are derived. We analyze the model parameter range and specify when a Vainshtein mechanism is possible.…
We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vectors. The solutions of the Einstein field equations examined specifically for five different set of spacetime. We calculate the…
Minkowski space is shown to be globally stable as a solution to the massive Einstein--Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying…
We determine the maximal number of systoles among all spheres with $n$ punctures endowed with a complete Riemannian metric of finite area.
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
We prove a global H\"older stability estimate for a hybrid inverse problem combining microwave imaging and ultrasound. The principal features of this result are that we assume to have access to measurements associated to a single, arbitrary…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to…
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem…