Related papers: Total stability functions for type $\mathbb{A}$ qu…

We study stability conditions on the derived category of a finite connected acyclic quiver. We prove that, for any stability condition on the derived category, its heart can be obtained from an algebraic heart by a rotation of phases.…

We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is…

Let X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability…

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…

The semi-stable ChowHa of a quiver with stability is defined as an analog of the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups of semi-stable loci in representation varieties of quivers.…

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the…

We prove that the Minkowski spacetime is stable at nonlinear level and to all perturbative orders in the gravitational perturbation in a general class of nonlocal gravitational theories that are unitary and finite at quantum level.

We prove an abstract infinite dimensional KAM theorem, which could be applied to prove the existence and linear stability of small-amplitude quasi-periodic solutions for one dimensional forced Kirchhoff equations with periodic boundary…

We prove a quantitative stability result for the Brunn-Minkowski inequality: if $|A|=|B|=1$, $t \in [\tau,1-\tau]$ with $\tau>0$, and $|tA+(1-t)B|^{1/n}\leq 1+\delta$ for some small $\delta$, then, up to a translation, both $A$ and $B$ are…

We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity…

We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…

We establish a lower bound on the total mass of the time slices of (n + 1)-dimensional asymptotically flat standard static spacetimes under the timelike convergence condition. The inequality can be viewed equivalently as a Minkowski-type…

We consider the $s$-fractional Klein-Gordon equation with space-dependent damping on $\mathbb{R}^d$. Recent studies reveal that the so-called geometric control conditions (GCC) are closely related to semigroup estimates of the equation.…

We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be…

We investigate the stability of equilibrium-induced optimal values with respect to (w.r.t.) reward functions $f$ and transition kernels $Q$ for time-inconsistent stopping problems under nonexponential discounting in discrete time. First,…

The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a…

We propose a notion of multi-scale stability conditions with the goal of providing a smooth compactification of the quotient of the space of projectivized Bridgeland stability conditions by the group of autoequivalence. For the case of the…

Complex scalar fields charged under a global U(1) symmetry can admit non-topological soliton configurations called Q-balls which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

For a wide class of linear Hamiltonian operators we develop a general criterion that characterizes the unstable eigenvalues as the zeros of a holomorphic function given by the determinant of a finite-dimensional matrix. We apply the latter…