相关论文: Isolated singularities, smooth orders and Auslande…
In this article we consider the classical singular integral operator over a local field with rough kernels. We study the boundedness of such an operator on different function spaces by relaxing the smoothness condition on kernels.
We consider the Kepler problem on surfaces of revolution that are homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge-Lentz…
Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_X-coherent D_X-modules) on X without relying on…
This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
Let $\mathbf{k}$ be an algebraically closed field, let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra, and let $\widehat{\Lambda}$ be the repetitive algebra of $\Lambda$. For the stable category of finitely generated left…
We prove generic regularity and Uhlenbeck-type compactification theorems for the moduli spaces of PU(2)-monopoles. Generic regularity is NOT obtained in the usual way (by applying Sard theorem to a smooth parameterized moduli space), since…
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
Model-theoretic aspects of exotic smoothness were studied long ago uncovering unexpected relations to noncommutative spaces and quantum theory. Some of these relations were worked out in detail in later work. An important point in the…
We study rational double points over algebraically closed fields in arbitrary characteristics and completely classify the indecomposable objects in their singularity categories, which correspond to the vertices in their Auslander-Reiten…
In this paper we construct odd finitely summable spectral triples based on length functions of bounded doubling on noncommutative solenoids. Our spectral triples induce a Leibniz Lip-norm on the state spaces of the noncommutative solenoids,…
We prove a general form of the regularity theorem for uniformity norms, and deduce an inverse theorem for these norms which holds for a class of compact nilspaces including all compact abelian groups, and also nilmanifolds; in particular we…
We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
Mather and Yau showed that an isolated complex hypersurface singularity is completely determined by its moduli algebra. It is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and,…
We first generalize classical Auslander-Reiten duality for isolated singularities to cover singularities with a one-dimensional singular locus. We then define the notion of CT modules for non-isolated singularities and we show that these…
The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are…
We classify the possible ramification data and etale local structure of orders over surfaces with canonical singularities.
We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…
We discuss a particular class of rational Gorenstein singularities, which we call symplectic. A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V…
A detailed study of uniformly regular Riemannian manifolds and manifolds with singular ends is carried out in this paper. Such classes of manifolds are of fundamental importance for a Sobolev space solution theory for parabolic evolution…