Metrization of Compact Convex Sets.
m-families and Common Transversals
Minimal fixing systems for convex bodies.
Minimal pairs of bounded closed convex sets
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.
Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces
The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.
Minimal pairs of compact convex sets
Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives...
Minimal pairs representing selections of four linear functions in .
Minimal sets of vectors which generate with excess
Minimal spherical shells and linear semi-infinite optimization.
Minimal surfaces shells containing a convex surface in Minkowski space.
Minimal-Energy Clusters of Hard Spheres.
Minimality in asymmetry classes
We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Minimax equalities by reconstruction of polytopes.
Minimax inequality of Ky Fan type in -spaces with applications.
Minimum Area of Circumscribed Polygons.
Minimum Dissection of a Rectilinear Polygon with Arbitrary Holes into Rectangles.
Minimum Ideal Triangulations of Hyperbolic 3-Manifolds.
Minimum Steiner Trees in Normed Planes.
Minimum-area axially symmetric convex bodies containing a triangle and its measure of axial symmetry.