Convex hull of extreme points in flat Riemannian manifolds

Flat Homogeneous Pseudo-Riemannian Manifolds

The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete fiat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbit...

On the convex hull of random points in a polytope

'This research was sponsored by the National Science Foundation under Grant No. ECS-8418392. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation or the US Government. On the Convex Hull of Random Points in a Polytope R e x A . D w y e r * ...

Extreme Points of Polar Convex Sets

The Structure of Compact Ricci-flat Riemannian Manifolds

where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentiall...

Area and Perimeter of the Convex Hull of Stochastic Points

Given a set P of n points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset S of P . The random subset S is formed by drawing each point p of P independently with a given rational probability πp. For both measures of the convex hull, we show that it is #P-hard to compute the probability that the m...