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Concept

Carathéodory's theorem (convex hull)

Related publications (24)

Order Types of Convex Bodies

We prove a Hadwiger transversal-type result, characterizing convex position on a family of non-crossing convex bodies in the plane. This theorem suggests a definition for the order type of a family of convex bodies, generalizing the usual definition of ord ...

2011

Tangencies between families of disjoint regions in the plane

János Pach

Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only ...

2010

Points surrounding the origin

János Pach

Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-emp ...

Springer-Verlag2008

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments ...

2008