相关论文: A new look at convexity and pseudoconvexity

This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…

We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.

We prove that a pseudoholomorphic diffeomorphism between two almost complex manifolds with boundaries satisfying some pseudoconvexity type condition cannot map a pseudoholomorphic disc in the boundary to a single point. This can be viewed…

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.

We characterize the diacriticals of special pencils. We also initiate higher dimensional dicritical theory.

A new family of maximal curves over a finite field is presented and some of their properties are investigated.

We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.

Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…

The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…

Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…

Let $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly…

We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In…

We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…

We study convex subsets of buildings, discuss some structural features and derive several characterizations of buildings.

In this paper, we will use investigate the existence of compactifications with particular convergence properties - pseudoradial, radial, sequential and Fr\'echet-Urysohn - through the use of spoke systems.

New types of maximal symplectic partial spreads are constructed.

We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…