Related papers: Stability and instability issues of the Weinstock …

We prove a new version of Bogomolov's inequality on normal proper surfaces. This allows to construct Bridgeland's stability condition on such surfaces. In particular, this gives the first known examples of stability conditions on…

Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…

A stability version of the Blaschke-Santal\'o inequality and the affine isoperimetric inequality for convex bodies of dimension n>2 is proved. The first step is the reduction to the case when the convex body is o-symmetric and has axial…

In this paper, we prove a stability result for an elastodynamic system with acoustic boundary conditions and localized internal damping, defined in a bounded domain $\Omega$ of $\mathbb{R}^3$. Here, the internal damping is only assumed to…

We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…

We investigate the geometric properties of Steklov eigenfunctions in smooth manifolds. We derive the refined doubling estimates and Bernstein's inequalities. For the real analytic manifolds, we are able to obtain the sharp upper bound for…

Let $E\subset \mathbb R^n$, $n\ge 2$, be a set of finite perimeter with $|E|=|B|$, where $B$ denotes the unit ball. When $n=2$, since convexification decreases perimeter (in the class of open connected sets), it is easy to prove the…

We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin's overdetermined problem in spaceforms. Secondly, we prove stability theorems for…

We study the Clifford type inequality for a particular type of curves $C_{2,2,5}$, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable…

We consider the dependence of non-zero Steklov eigenvalues on smooth perturbations of the domain boundary. We prove that these eigenvalues are generically simple under such boundary perturbations. This result complements our previous work…

Let us say that an $n$-sided polygon is semi-regular if it is circumscriptible and its angles are all equal but possibly one, which is then larger than the rest. Regular polygons, in particular, are semi-regular. We prove that semi-regular…

We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the…

Let $\Omega\subset \mathbb{R}^d$ be an open set of finite measure and let $\Theta$ be a disjoint union of two balls of half measure. We study the stability of the full Dirichlet spectrum of $\Omega$ when its second eigenvalue is close to…

The existence and stability conditions of Einstein static universe against homogeneous scalar perturbations in the context of Lyra geometry is investigated. The stability condition is obtained in terms of the constant equation of state…

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…

The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the…

In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…

Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…

We prove the conjectural Bogomolov-Gieseker type inequality for tilt slope stable objects on each Fano threefold X of Picard number one. Based on the previous works on Bridgeland stability conditions, this induces an open subset of…

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi $ defined on a fixed reference domain $\Omega$. Given two…