Related papers: Stability for a second type partitioning problem
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
Since the early years of General Relativity, understanding the long-time behavior of the cosmological solutions of Einstein's vacuum equations has been a fundamental yet challenging task. Solutions with global symmetries, or perturbations…
Given a manifold with boundary, one can consider the space of subsurfaces of this manifold meeting the boundary in a prescribed fashion. It is known that these spaces of subsurfaces satisfy homological stability if the manifold has at least…
We show the existence of stable bound orbits for the massive and massless particles moving in the simplest microstate geometry spacetime in the bosonic sector of the five-dimensional minimal supergravity. In our analysis, reducing the…
The possible existence of (meta-) stable de Sitter vacua in string theory is of fundamental importance. So far, there are no fully stable solutions where all effects are under perturbative control. In this paper we investigate the presence…
In this paper, we present sharp stability results for various reverse isoperimetric problems in $\mathbb R^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for $\lambda$-convex bodies -- convex bodies with…
We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived…
It is possible to condense a macroscopic number of bosons into a single mode. Adding interactions the question arises whether the condensate is stable. For repulsive interaction the answer is positive with regard to the ground-state, but…
This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
We consider the consequences of keeping the total surface fixed for a polydisperse system of $N$ hard spheres. In contrast with a similar model (J. Zhang {\it et al.}, J. Chem. Phys. {\bf 110}, 5318 (1999)), the Percus-Yevick and Mansoori…
The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this…
We present some non-topological static wall solutions in two-Higgs extensions of the standard model. They are classically stable in a large region of parameter space, compatible with perturbative unitarity and with present phenomenological…
We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…
The inflow problem of full compressible Navier-Stokes equations is considered on the half line $(0,+\infty)$. Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state…
The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
The theory of turbulent Newtonian fluids turns out that the choice of the boundary condition is a relevant issue, since it can modify the behavior of the fluid by creating or avoiding a strong boundary layer. In this work we study…
Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…
We consider the 2D Euler equation of incompressible fluids on a strip and prove the stability of the rectangular stationary state.