The problem of polygons with hidden vertices.
The Quotient Space of C P (2) by Complex Conjugation is the 4-Sphere.
The rank of extreme positive operators on polyhedral cones
The refinement and reverse of a geometric inequality.
The Reverse Isoperimetric Problem for Gaussian Measure.
The simultaneous existence of linear functionals
The size of the shadow boundary pojection.
The skeleta of convex bodies
The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.
The space of maximal convex sets
The Steiner Minimal Network for Convex Configurations.
The sum of two plane convex C... sets is not always C...
The Thinnest Holding-Lattice of a Set.
The Worm Problem of Leo Moser.
Théorème d'approximation et espaces de Hopf.
Theorems of the alternative for cones and Lyapunov regularity of matrices
Standard facts about separating linear functionals will be used to determine how two cones and and their duals and may overlap. When is linear and and are cones, these results will be applied to and , giving a unified treatment of several theorems of the alternate which explain when contains an interior point of . The case when is the space of Hermitian matrices, is the positive semidefinite matrices, and yields new and known results about the existence of block diagonal...
Theorems on equipartition of a continuous mass distribution.
Theorems on the Existence of Separating Surfaces.
There Exist 6n/13 Ordinary Points.
There is no cogenerator of totally convex spaces
Thin-shell concentration for convex measures
We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.