Related papers: Generalized convex sets and shadows problem
In the present work, the problem about shadow, generalized on domains of space $\mathbb{R}^n$, $n\le 3$, is investigated. Here the shadow problem means to find the minimal number of balls satisfying some conditions an such that every line…
We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.
The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets is developed. In particular, it is shown that this concept is useful in the study of best…
We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.
The following work presents a sufficiently general method for finding the parameters that characterise self-gravitating compact objects when their shadow contour is explicitly set. This method can be used in various algorithms to analyse…
We explore the shadow of certain class of rotating traversable wormholes within classical general relativity. The images depend on the angular momentum of the wormhole, and the inclination angle of the observer. We compare the results with…
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
Single-view point cloud completion aims to recover the full geometry of an object based on only limited observation, which is extremely hard due to the data sparsity and occlusion. The core challenge is to generate plausible geometries to…
This paper examines the relationship between shadowing phenomena and the continuity properties of $\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower)…
We prove that a closed convex subset $C$ of a complete linear metric space $X$ is polyhedral in its closed linear hull if and only if no infinite subset $A\subset X\backslash C$ can be hidden behind $C$ in the sense $[x,y]\cap C\not =…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.
We study the closure of the convex hull of a compact set in a complete CAT(0) space. First we give characterization results in terms of compact sets and the closure of their convex hulls for locally compact CAT(0) spaces that are either…
The Gauss image problem for convex bodies asks for the existence of a convex body that "links" two given measures on the unit sphere in a certain way. We treat here a corresponding question for pseudo-cones, that is, for unbounded closed…
We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…
In this article a class of closed convex sets in the Euclidean $n$-space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\cite{Lay:1982} to a class of closed non-compact convex sets is…
Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative…
Isoperimetric inequalities have been studied since antiquity, and in recent decades they have been studied extensively on discrete objects, such as the hypercube. An important special case of this problem involves bounding the size of the…