Related papers: A criterion for slope 1 homological stability
We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional.
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be…
We extend the result of D. Phillips (On one-homogeneous solutions to elliptic systems in two dimensions. C. R. Math. Acad. Sci. Paris 335 (2002), no. 1, 39-42) by showing that one-homogeneous solutions of certain elliptic systems in…
We establish the Hyers-Ulam stability of certain linear first-order differential equations with singularities. We then extend these results to higher-order singular linear differential equations that can be written with these first-order…
This is the second part of a series of papers proving the nonlinear stability of a one-parameter family of continuous self-similar $C^{1,\alpha}$ naked singularity solutions, with $0<\alpha\ll1$, to the spherically symmetric Einstein-scalar…
In this paper, we show the orbital stability of solitons arising in the cubic derivative nonlinear Schrodinger equations. We consider the zero mass case that is not covered by earlier works [8, 3]. As this case enjoys L^2 scaling…
We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
We prove that certain families of Coxeter groups and inclusions $W_1\hookrightarrow W_2\hookrightarrow...$ satisfy homological stability, meaning that in each degree the homology $H_\ast(BW_n)$ is eventually independent of $n$. This gives a…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
We give two characterisations of when a map-germ admits a 1-parameter stable unfolding, one related to the $\mathscr K_e$-codimension and another related to the normal form of a versal unfolding. We then prove that there are infinitely many…
We construct infinite families of nonzero classes in $H_d(GL_n(F_2);F_2)$ along lines of the form $d =\frac{2}{3}n +$(constant), thereby showing that the known slope $\frac{2}{3}$-stability for these homology groups are optimal. Using the…
The stability and the index of complete one-sided minimal surfaces of certain three-dimensional Riemannian manifolds with positive scalar curvature are studied.
A complex algebraic surface $S$ is a $\mathbb{Q}$-homology plane if $H_{i}(S,\mathbb{Q})=0$ for $i>0$. The Negativity Conjecture of Palka asserts that $\kappa(K_{X}+\tfrac{1}{2}D)=-\infty$, where $(X,D)$ is a log smooth completion of $S$.…
We prove a homological stability theorem for unlinked circles in $3$-manifolds and give an application to certain groups of diffeomorphisms of 3-manifolds.
We establish nonlinear $H^2\cap L^1 \to H^2$ stability with sharp rates of decay in $L^p$, $p\geq 2$, of general hydraulic shock profiles, with or without subshocks, of the inviscid Saint-Venant equations of shallow water flow, under the…
In this article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and…
In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases.…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
In this paper we discuss the stability of stochastic differential equations and the interplay between the moment stability of a SDE and the topology of the underlying manifold. Sufficient and necessary conditions are given for the moment…