On the Euler Characteristic of Finite Unions of Convex Sets.
On the geometry of convex reflectors
In this paper we consider a special class of convex hypersurfaces in Euclidean space which arise as weak solutions to some inverse problems of recovering reflectors from scattering data. For this class of hypersurfaces we study the notion of the focal function which, while sharing the important convexity property with the classical support function, has the advantage of being exactly the "right tool" for such inverse problems. We also discuss briefly the close analogy between one such inverse problem...
On the geometry of and .
On the Intermediate Area Functions of Convex Bodies.
On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)
Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K instead of the whole space as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous...
On the maximal operator associated to a convex body in Rn.
On the multiplicity points of monotone operators on separable Banach spaces. II.
On the multiplicity points of monotone operators on separable Banach spaces
On the points of multiplicity of monotone operators
On the semicontinuity of curvatures.
On the set of weighted least squares solutions of systems of convex inequalities
On the shadows and the sections of convex sets.
On the Sobolev distance of convex bodies.
On the structure of convex sets with applications to the moduli of spherical minimal immersions.
On the Sum of a Zonotope and an Ellipsoid
On the Volume of Equichordal Sets.
On the ψ₂-behaviour of linear functionals on isotropic convex bodies
The slicing problem can be reduced to the study of isotropic convex bodies K with , where is the isotropic constant. We study the ψ₂-behaviour of linear functionals on this class of bodies. It is proved that for all θ in a subset U of with measure σ(U) ≥ 1 - exp(-c√n). However, there exist isotropic convex bodies K with uniformly bounded geometric distance from the Euclidean ball, such that . In a different direction, we show that good average ψ₂-behaviour of linear functionals on an isotropic...
On Tucker's key theorem.
On Two Conjectures of Franz Hering About Convex Surfaces.
On weighted parallel volumes.