Une deuxième surface à courbure moyenne prescrite s'appuyant sur une courbe donnée
Une famille d’inégalités pour les ensembles convexes du plan
Nous considérons une famille de fonctions ne dépendant que de la forme d’un ensemble convexe du plan. Nous en donnons des majorations faisant intervenir le plus petit rapport des rayons des couronnes qui contiennent la frontière de ce convexe.
Une inégalité isopérimétrique en courbure négative d'après Christopher B. Croke
Une relation entre diamètre extrinsèque, intégrale de la courbe de Gauss et inradius pour les hypersurfaces localement convexes d'un espace euclidien.
Ungleichungen für die Quermassenintegrale polarer Körper.
Uniform decompositions of polytopes
We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the...
Uniform properties of collections of convex bodies.
Unilateral tilings of the plane with squares of three sizes.
Unimodular covers of multiples of polytopes.
Unimodular Pisot substitutions and their associated tiles
Let be a unimodular Pisot substitution over a letter alphabet and let be the associated Rauzy fractals. In the present paper we want to investigate the boundaries () of these fractals. To this matter we define a certain graph, the so-called contact graph of . If satisfies a combinatorial condition called the super coincidence condition the contact graph can be used to set up a self-affine graph directed system whose attractors are certain pieces of the boundaries . From this graph...
Unique reducibility of subsets of commutative topological groups and semigroups.
Uniqueness and symmetry in problems of optimally dense packings.
Uniqueness of Cartesian Products of Compact Convex Sets
Let , i∈ I, and , j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of onto . We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of onto , i∈ I.
Uniqueness of the spherical code.
Unit Squares Intersecting All Secants of a Square.
Unit-distance graphs, graphs on the integer lattice and a Ramsey type result.
Universal container for packing rectangles
The aim of the paper is to find a rectangle with the least area into which each sequence of rectangles of sides not greater than 1 with total area 1 can be packed.
Universal counting of lattice points in polytopes.
Universal tessellations.
All maps of type (m,n) are covered by a universal map M(m,n) which lies on one of the three simply connected Riemann surfaces; in fact M(m,n) covers all maps of type (r,s) where r|m and s|n. In this paper we construct a tessellation M which is universal for all maps on all surfaces. We also consider the tessellation M(8,3) which covers all triangular maps. This coincides with the well-known Farey tessellation and we find many connections between M(8,3) and M.
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