Related papers: Stable configurations of repelling points on compa…
This is an expanded version of [arXiv:1107.4836v1 [math.DS]]. Using techniques from [Chapter XI, The Selberg Trace Formula, in Eigenvalues in Riemannian Geometry, by Isaac Chavel], in which a differential-geometrically intrinsic treatment…
This paper extends the stability calculations carried out for a spherical particle [Eur. Phys. J. B, vol. 37 (2004) or arXiv: cond-mat/0401404] to the case of a cylindrical inclusion.
It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases
A construction of a robust family of compact inertial manifolds is presented. The result aims to complete an analysis of certain types of attracting sets for a class of dissipative infinite dimensional dynamical systems. Application to a…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
We study the stability of the embeddability of compact 2-concave CR manifolds in complex manifolds under small horizontal perturbations of the CR structure.
One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and…
Many Euclidean Einstein manifolds possess continuous symmetry groups of at least one parameter and we consider here a classification scheme of $d$ dimensional compact manifolds based on the existence of such a one parameter group in terms…
We consider an electrostatic attractive-repulsive differential system in the nonnegative quadrant. Under some condition on the constants there exists a unique global solution. The main difficulty is to prove uniqueness when starting at the…
The reduced system in the problem of the inertial motion of a rigid body with a fixed point (the Euler case) is equivalent, by the Maupertuis principle, to some geodesic flow on the 2-sphere. We describe the phase topology of this case…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
We provide a sufficient condition for the local stability of closed Einstein manifolds of positive Ricci curvature under the Ricci iteration in terms of the spectrum of the Lichnerowicz Laplacian acting on divergence-free tensor fields. We…
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of…
We prove the stability of the equivariant embedding of compact strictly pseudoconvex CR manifolds with transversal CR circle action under circle invariant perturbations of the CR structures.
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
The focusing critical wave equation in three dimensions exhibits a special class of static solutions which are linearly unstable. These solutions decay like an inverse first power. We construct small codimension one stable manifolds in the…