Compact convex bodies with one curvature measure near the surface measure.
Compact convex sets of the plane and probability theory
The Gauss−Minkowski correspondence in ℝ2 states the existence of a homeomorphism between the probability measures μ on [0,2π] such that ∫ 0 2 π e ix d μ ( x ) = 0 and the compact convex sets (CCS) of the plane with perimeter 1. In this article, we bring out explicit formulas relating the border of a CCS to its probability measure. As a consequence, we show that some natural operations on CCS – for example, the Minkowski sum – have natural translations in terms of probability measure operations,...
Compact hyperbolic tetrahedra with non-obtuse dihedral angles.
Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of RE. If C has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andreev did not consider tetrahedra, the only polyhedra having fewer than five faces, by demonstrating that the...
Compact packings in the Euclidean space
Compactness and countable compactness in weak topologies
A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact....
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Compacts de fonctions de première classe
Comparing the relative volume with the relative inradius and the relative width.
Comparison between the generalized mean curvature according to Allard and Federer's mean curvature measure
Compatible complex structures on twistor space
Let be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space admits a natural metric. The aim of this article is to study properties of complex structures on which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space .
Compensated convexity and its applications
Complément de Schur et sous-différentiel du second ordre d'une fonction convexe.
Complete extension of a convex function
Complete systems of inequalities.
Complex Hadamard matrices and the spectral set conjecture.
By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.
Complexes of Directed Trees of Complete Multipartite Graphs
Complexes Whose Boundaries Cannot Be Pushed Around.
Complexity aspects of the Helly property: graphs and hypergraphs.
Computation of Bett Numbers of Monomial Ideals Associated with Stacked Polytopes.
Computer Generated Islamic Star Patterns