An extension of the isoperimetric inequality on the sphere.
An illustrated theory of hyperbolic virtual polytopes
The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.
An incomplete Voronoi tessellation
This paper presents distributional properties of a random cell structure which results from a growth process. It starts at the points of a Poisson point process. The growth is spherical with identical speed for all points; it stops whenever the boundaries of different cells have contact. The whole process finally stops after time t. So the space is not completely filled with cells, and the cells have both planar and spherical boundaries. Expressions are given for contact distribution functions,...
An inequality for convex curves in the plane.
An Inequality for the Volume of Inscribed Ellipsoids.
An integral formula related to inner isoptics
An integral geometric theorem for simple valuations.
An isomorphic Dvoretzky's theorem for convex bodies
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.
An isoperimetric partition problem.
An isoperimetric problem for tetrahedra.
An O (n log n) Algorithm for Computing the Link Center of a Simple Polygon.
An O(n log n) Algorithm for the Voronoi Diagram of a Set of Simple Curve Segments.
An Optimal Convex Hull Algorithm in Any Fixed Dimension.
An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems.
We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding to Gale, Farkas, Gordan and Motzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.
An upper bound for a sequence of cevian inequalities.
Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten.
Approximately generalized convex functions.
Approximating 3-dimensional convex bodies by polytopes with a restricted number of edges.
Approximating the Ball by a Minkowski Sum of Segments with Equal Length.
Approximating the Volume of Convex Bodies.