Related papers: Sliding stability and uniqueness for the set YXY
We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea…
Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for different finite element schemes on a simplified version of the…
In this paper, we study stability properties of solutions to scalar conservation laws with a class of non-convex fluxes. Using the theory of $a$-contraction with shifts, we show $L^2$-stability for shocks among a class of large…
Based on the Decay and Fission Conjecture, we provide a classification of unitary quivers whose 3d $\mathcal{N}=4$ Coulomb branches exhibit isolated singularities. This yields the complete list of isolated conical symplectic singularities…
We study the rational homology of the Deligne--Mumford compactification $\overline{\mathcal M}_{g,n}$ of the moduli space of stable curves via a family of Morse functions, namely the $\text{sys}_T$ functions. Exploiting the geometric and…
We have examined the stability of a sequence of oblate elliptical galaxy models having the Stackel form suggested by Kuz'min & Kutuzov. We have employed the 2-integral DFs given by Dejonghe & de Zeeuw for which flattened non-rotating models…
We study families of spherical metrics on the flat torus $E_{\tau}$ $=$ $\mathbb{C}/\Lambda_{\tau}$ with blow-up behavior at prescribed conical singularities at $0$ and $\pm p$, where the cone angle at $0$ is $6\pi$, and at $\pm p$ is…
The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show that globally $m-$fold symmetric vortex…
Stability analysis of discrete-time switched systems under minimum dwell-time is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions…
In this short note, we prove a uniqueness result for small entropy self-expanders asymptotic to a fixed cone. This is a direct consequence of the mountain-pass theorem and the integer degree argument proved by J. Bernstein and L. Wang.
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
This paper concerns the formation of singularities in the classical $(5+1)$-dimensional, co-rotational Skyrme model. While it is well established that blowup is excluded in $(3+1)$-dimensions, nothing appears to be known in the higher…
We investigate the decomposition of a set $X$, which positively spans the Euclidean space $\mathbb{R}^{d}$ into a set of minimal positive bases, we call simplices, and into maximal sets positively spanning pointed cones, i.e. cones with…
The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface…
While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as…
We show that a uniformly Euclidean metric with isolated singularity on $M^n = T^n \# M_0$, where $4\leq n\leq 7$ or $n\geq 4$, $M_0$ spin, and nonnegative scalar curvature on the smooth part is Ricci flat and extends smoothly over the…
We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…
In this paper we study 4d gradient steady Ricci solitons, which are weak $\kappa$-solutions, and admit O(3)-symmetry. Under a weak curvature decay condition, we find precise geometric asymptotics of such solitons, which are similar to those…
The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…
Vortex singularities in speckle patterns formed from random superpositions of waves are an inevitable consequence of destructive interference and are consequently generic and ubiquitous. Singularities are topologically stable, meaning they…