Related papers: Limit Models in Strictly Stable Abstract Elementar…

We investigate the singularities and boundedness of a special kind of algebraic varieties so-called stable minimal models, which are constructed and studied by Birkar. Given a klt stable minimal model with bounded relative volume, if we fix…

Local models are schemes, defined in terms of linear algebra, that were introduced by Rapoport and Zink to study the \'etale-local structure of integral models of certain PEL Shimura varieties over p-adic fields. A basic requirement for the…

Local models are schemes, defined in terms of linear-algebraic moduli problems, which give \'etale-local neighborhoods of integral models of certain p-adic PEL Shimura varieties defined by Rapoport and Zink. In the case of a unitary…

This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup…

In this paper, we study a stability transfer theorem in d-tame Metric Abstract Elementary classes, in a similar way as in [BaKuVa], but using superstability-like assumptions which involves a new independence notion (Tame Independence)…

We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…

Let $M$ and $N$ be smooth (real or complex) manifolds, and let $M$ be equipped with some Riemannian metric. A continuous map $f\colon M\longrightarrow N$ admits a local $k$-multiplicity if, for every real number $\omega >0$, there exist $k$…

We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where $n$ is even. For these varieties, we construct smooth $p$-adic integral models for $s=1$ and regular $p$-adic integral models for $s=2$ and $s=3$ over…

Let K be an abstract elementary class of models. Assume that there are less than the maximal number of models in K_{\lambda^{+n}} (namely models in K of power \lambda^{+n}) for all n. We provide conditions on K_\lambda, that imply the…

We study semilinear elliptic equations \begin{equation*} \begin{cases} -\Delta u = f(u) & \text{in } \Omega, \\ \partial_\nu u = 0 & \text{on } \partial\Omega, \end{cases} \end{equation*} with homogeneous Neumann boundary conditions in…

We verify that for all $n \geq 3$ and $2 \leq k \leq n+1$, the standard $k$-bubble clusters, conjectured to be minimizing total perimeter in $\mathbb{R}^n$, $\mathbb{S}^n$ and $\mathbb{H}^n$, are stable -- an infinitesimal regular…

Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems of metrics in a same conformal class that fixes the boundary and satisfy certain integral conditions on the the scalar curvatures and the mean…

This paper is a contribution to "neo-stability" type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly…

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable…

We study limit models in the abstract elementary class of modules with embeddings as algebraic objects. We characterize parametrized noetherian rings using the degree of injectivity of certain limit models. We show that the number of limit…

Mapping class groups satisfy cohomological stability. In this note we show how results by Bestvina and Fujiwara imply that the bounded cohomology does not stabilize, additionally we show that stabily polynomials in the Mumford-Morita-Miller…

We study the geometry of unitary Shimura varieties without assuming the existence of an ordinary locus. We prove, by a simple argument, the existence of canonical subgroups on a strict neighborhood of the $\mu$-ordinary locus (with an…

The results in this paper are in a context of abstract elementary classes identified by Shelah and Villaveces in which the amalgamation property is not assumed. The long-term goal is to solve Shelah's Categoricity Conjecture in this…

In various supersymmetric extensions of the Standard Model there appear non-topological solitons due to the existence of U(1) global symmetries associated with Baryon and/or Lepton quantum numbers. Trilinear couplings (A-terms) in the…

We give a survey of the known connections between regularity conditions and amenability conditions in the setting of uniform algebras. For a uniform algebra $A$ we consider the set, $A_{lc}$, of functions in $A$ which are locally constant…