Mixture Sets and Convex Sets
Moduli of rotundity and smoothness for convex bodies.
Monotone Valuations on the Space of Convex Functions
We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.
Monotonic rearrangements of functions with small mean oscillation
We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous" ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named α-extension.
Monotonicity of the maximum of inner product norms
Let be the field of real or complex numbers. In this note we characterize all inner product norms on for which the norm on is monotonic.
More on exposed points and extremal points of convex sets in and Hilbert space
Let be a separable real Hilbert space, with , and let be convex and closed in . Let be a collection of linear -subspaces of . A point is called exposed by if there is a so that . We show that, under some natural conditions, can be reconstituted as the convex hull of the closure of all its exposed by points whenever is dense and . In addition, we discuss the question when the set of exposed by some points forms a -set.
More on k-Sets of Finite Sets in the Plane.
More than first-order developments of convex functions: primal-dual relations.
Multiapplications boréliennes à valeurs convexes de
Multiobjective problems of convex geometry.
Multiplication of convex sets in C(K) spaces
Let C(K) denote the Banach algebra of continuous real functions, with the supremum norm, on a compact Hausdorff space K. For two subsets of C(K), one can define their product by pointwise multiplication, just as the Minkowski sum of the sets is defined by pointwise addition. Our main interest is in correlations between properties of the product of closed order intervals in C(K) and properties of the underlying space K. When K is finite, the product of two intervals in C(K) is always an interval....
Náměty k středoškolské geometrii (Geometrické nerovnosti)
n-ary transit functions in graphs
n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also n-ary all paths transit function is considered.
Nearly All Convex Bodies Are Smooth and Strictly Convex.
Nearly regular cell-decompositions of orientable 2-manifolds with at most two exceptional cells
Některé vlastnosti pravidelných těles vypuklých
Neuere Studien über Gitterpolygone.
New Applications of Random Sampling in Computational Geometry.
New lower bounds for Heilbronn numbers.
New volume ratio properties for convex sym-metric bodies in IRn.