Related papers: Stability of Coassociative Conical Singularities

Let $S$ be a complete intersection of a smooth quadric 3-fold $Q$ and a hypersurface of degree $d$ in ${\mathbb P}^4$. In this paper we analyze GIT stability of $S$ with respect to the natural $G=SO(5, {\mathbb C})$-action. We prove that if…

The stability of nonlinear waves on curved surfaces is a problem of widespread interest across physics. Here, we establish the stability criteria for dark solitons on a spherical Bose-Einstein condensate. We demonstrate a sharp instability…

We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of…

Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3]…

We establish an interesting connection between Morin singularities and stable homotopy groups of spheres. We apply this connection to computations of cobordism groups of certain singular maps. The differentials of the spectral sequence…

We study the stability properties of nodal sets of Laplace eigenfunctions on compact manifolds under specific small perturbations. We prove that nodal sets are fairly stable if said perturbations are relatively small, more formally,…

We study sufficient conditions for stability and recurrence in a class of singularly perturbed stochastic hybrid dynamical systems. The systems considered combine multi-time-scale deterministic continuous-time dynamics, modeled by…

Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…

We show how the small perturbations of a linear cocycle have a relative rotation number associated with an invariant measure of the base dynamics an with a $2$-dimensional bundle of the finest dominated splitting (provided that some…

We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove…

We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…

We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…

This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we…

In this paper, we present new results regarding the orbital stability of solitary standing waves for the general fourth-order Schr\"odinger equation with mixed dispersion. The existence of solitary waves can be determined both as minimizers…

We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on an accurate description of the pointwise…

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the $n$ dimensional case, the zero solution is globally…

We use perturbations in order to study the stability of the Cauchy Horizon in a Reissner-Nordstr\"om space-time. The perturbations are either scalar or gravitational, and indicate some strong instabilities.