Lattice Points in Lattice Polytopes.
Lattice points in Minkowski sums.
Lattice Points on Convex Curves.
Lattice tilings by cubes: Whole, notched and extended.
Lattice-Free Polytopes and Their Diameter.
Layered circle packings.
Least deviation decomposition with respect to a pair of convex sets.
Length-preserving deformations of closed plane curvesc
Les cinq métamorphoses des surfaces pavées
Les (e...,...,e...)-convexes de R...; la proprieté d'intersection et les filtres maximaux de convexes.
Light classes of generalized stars in polyhedral maps on surfaces
A generalized s-star, s ≥ 1, is a tree with a root Z of degree s; all other vertices have degree ≤ 2. denotes a generalized 3-star, all three maximal paths starting in Z have exactly i+1 vertices (including Z). Let be a surface of Euler characteristic χ() ≤ 0, and m():= ⎣(5 + √49-24χ( ))/2⎦. We prove: (1) Let k ≥ 1, d ≥ m() be integers. Each polyhedral map G on with a k-path (on k vertices) contains a k-path of maximum degree ≤ d in G or a generalized s-star T, s ≤ m(), on d + 2- m() vertices...
Light paths with an odd number of vertices in polyhedral maps
Let be a path on vertices. In an earlier paper we have proved that each polyhedral map on any compact -manifold with Euler characteristic contains a path such that each vertex of this path has, in , degree . Moreover, this bound is attained for or , even. In this paper we prove that for each odd , this bound is the best possible on infinitely many compact -manifolds, but on infinitely many other compact -manifolds the upper bound can be lowered to .
Limit shape of Jarník's polygonal curve is a circle
Limite d'hypersurfaces localement convexes.
Limits and colimits of convexity spaces
Linear combinations of partitions of unity with restricted supports
Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation with and a partition of unity subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction attains its extrema at vertices of P. Finally, a class of extremal functions on the metric space...
Linear programming duality and morphisms
In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....
Lipschitz continuous selectors. I: Linear selectors.
Lipschitz sums of convex functions
We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.
LNC points for m-convex sets.