A characterisation of the ellipsoid in terms of concurrent sections.
A characterization of convex calibrable sets in with respect to anisotropic norms
A contribution to the light field theory
A general geometric construction for affine surface area
Let K be a convex body in and B be the Euclidean unit ball in . We show that , where as(K) respectively as(B) is the affine surface area of K respectively B and , are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].
A Helmholtz-Lie Type Characterization of Ellipsoids, I .
A model for Toepliz operators in the space of entire functions of exponential type
A New Duality Result Concerning Voronoi Diagrams.
A normed space with the Beckman-Quarles property.
A note on convexly independent subsets of an infinite set of points.
A note on equality of functional envelopes
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in , , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
A Note on Sets of Constant Width
A note on the closedness of the convex hull and its applications.
A positive solution to the Busemann-Petty problem in .
A problem of Schinzel on lattice points
A quantitative isoperimetric inequality in n-dimensional space.
A refined Brunn-Minkowski inequality for convex sets
A representation for volume involving interior reach.
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
A short proof of Dvoretzky's theorem on almost spherical sections of convex bodies