Planning a Purely Translational Motion for a Convex Object in Two-Dimensional Space Using Generalized Voronoi Diagrams.
Poincaré Inequalities and Moment Maps
We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of -spaces in for .
Point derivations for Lipschitz functions andClarke's generalized derivative
Clarke’s generalized derivative is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed and fixed the function is continuous and sublinear in . It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz’s product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
Points extrêmaux dans un monoide affine semitopologique.
Points extrémaux d'un convexe compact de Rn appartenant à un réseau
Points extrémaux d'un simplexe compact métrisable
Points extrémaux et densité.
Points of infinitely many normals to convex surfaces.
Polarity of embedded and circumscribed ellipsoids.
Polygonizations of Point Sets in the Plane.
Polygons with hidden vertices.
Polyhedra inscribed and circumscribed to convex bodies.
Polyhedral approximation of convex sets with an application to large deviation probability theory.
Polyhedral Line Transversals in Space.
Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces
A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly one convex...
Polynomial selections and separation by polynomials
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
Polytope in lokalkonvexen Räumen.
Preassigning the Boundary of Diametrically-Complete Sets.
Presssigning the Shape for Bodies of Constant Width.
Produit tensoriel de deux cônes convexes saillants