The Convex Hull of a Typical Compact Set.
The Demyanov metric and some other metrics in the family of convex sets
We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
The determination of convex bodies from the size and shape of their projections and sections
We survey results concerning the extent to which information about a convex body's projections or sections determine that body. We will see that, if the body is known to be centrally symmetric, then it is determined by the size of its projections. However, without the symmetry condition, knowledge of the average shape of projections or sections often determines the body. Rather surprisingly, the dimension of the projections or sections plays a key role and exceptional cases do occur but appear to...
The Different Ways of Stabbing Disjoint Convex Sets.
The dimension of almost spherical sections of convex bodies
The Dimension Print of Most Convex Surfaces.
The dual Steiner formula for convex compacta.
The endomorphisms of the lattice of closed convex cones.
The Generic Contact of Convex Bodies with Circumscribed Homothets of a Convex Surface.
The intersection of convex transversals is a convex polytope.
The isoperimetric inequality for a pentagon in and its generalization in space
The linear control problem
The minimum mean width translation cover for sets of diameter one.
The plank problem for symmetric bodies.
The Quotient Space of C P (2) by Complex Conjugation is the 4-Sphere.
The rank of extreme positive operators on polyhedral cones
The Reverse Isoperimetric Problem for Gaussian Measure.
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.
Theorems on equipartition of a continuous mass distribution.
Transitivity Domains of Groups of Similarities.