Related papers: Stable Pairs and Coercive Estimates for The Mabuch…

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then…

In 1980, I. Morrison proved that slope stability of a vector bundle of rank 2 over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. Using the notion of balanced…

We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a…

We will present proofs for two conjectures stated in arXiv:1808.08073. The first one is that for an arbitrary manifold $W$, the homotopy classes of proper maps $W\times\mathbb{R}^n\to\mathbb{R}^{k+n}$ stabilise as $n\to\infty$, and the…

We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn Hoffman field can be extended continuously to the…

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

We investigate Chow stability of projective bundles P(E) where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarisations L, the pair (P(E),L) is Chow stable and…

We study quotients of mapping class groups (\Gamma_{g,1}) of oriented surfaces with one boundary component by terms of their Johnson filtrations, and we show that the homology of these quotients with suitable systems of twisted coefficients…

We construct stable manifolds for a class of degenerate evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kinetic shock and boundary layers to their limiting equilibrium…

This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9…

We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a…

In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.

Following the argument for diffeomorphisms by Galatius and Randal-Williams, we prove that homeomorphisms of 1-connected manifolds of even dimension at least 6 exhibit homological stability. We deduce similar results for PL homeomorphisms…

We prove that every proper subspace of the moduli space of stable surfaces with fixed volume over an algebraically closed field of characteristic p>5 is projective. As a consequence we also deduce that the same moduli space is projective…

We consider the K\"ahler-Ricci flow on a Fano manifold. We show that if the curvature remains uniformly bounded along the flow, the Mabuchi energy is bounded below, and the manifold is K-polystable, then the manifold admits a…

We prove that the stable manifold of every point in a compact hyperbolic invariant set of a holomorphic automorphism of a complex manifold is biholomorphic to a complex vector space, provided that a bunching condition, which is weaker than…

This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…

In this paper, we consider the preservation of stability by using the notion of Twisted stability. As applications, (1) we show that moduli spaces of vector bundles on K3 and abelian surfaces are irreducible, (2) we compute Hodge…

We study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if and only if they have the same w_2-type and their equivariant…