Mehrfache gitterförmige Kreis- und Kugelanordnungen.
Mehrfach-orthogonale Simplexe in Räumen konstanter Krümmung
Mesures de courbure des variétés lisses et des polyèdres
Mesures sur le cercle et convexes du plan
Methods of Perfect Coloring
Metric ellipses in Minkowski planes.
An ellipse in R2 can be defined as the locus of points for which the sum of the Euclidean distances from the two foci is constant. In this paper we will look at the sets that are obtained by considering in the above definition distances induced by arbitrary norms.
Metric entropy of convex hulls in Hilbert spaces
Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), , , by functions of the ’s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences .
Metric Entropy of Homogeneous Spaces
For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...
Metrically convex functions in normed spaces
Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.
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.