相关论文: Stability conditions on triangulated categories
We define $n$-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-$n$-angulations. We obtain a large class of examples of…
In this paper the new model of plastic deformation is constructed. For classification of plastic statuses the theory of knot is used.
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the…
This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the…
In this note we give a direct method to classify all stable forms on $\R^n$ as well as to determine their automorphism groups. We show that in dimension 6,7,8 stable forms coincide with non-degnerate forms. We present necessary conditions…
We propose a general method to construct new triangulated categories, relative stable categories, as additive quotients of a given one. This construction enhances results of Beligiannis, particularly in the tensor-triangular setting. We…
The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincare translation numbers that are widely used in dynamical systems. Motivated by…
Discrete derived categories were studied initially by Vossieck \cite{Vossieck} and later by Bobi\'nski, Gei\ss, Skowro\'nski \cite{BGS}. In this article, we define the CW complex of silting pairs for a triangulated category and show that it…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…
This paper deals with uniform stabilization of the damped wave equation. When the manifold is compact and the damping is continuous, the geometric control condition is known to be necessary and sufficient. In the case where the damping is a…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
We study the problem of when triangulated categories admit unique infinity-categorical enhancements. Our results use Lurie's theory of prestable infinity-categories to give conceptual proofs of, and in many cases strengthen, previous work…
We prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S^n x S^n, in the…
We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a…
The homology of configuration spaces of point-particles in manifolds has been studied intensively since the 1970s; in particular it is known to be stable if the underlying manifold is connected and open. Closely related to configuration…
This article deals with different generalizations of the discrete stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their…
As recently pointed out by Li and Xu, the definition of K-stability, and the author's proof of K-stability for cscK manifolds without holomorphic vector fields, need to be altered slightly: the Donaldson-Futaki invariant is positive for all…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…