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 On-Line Potato-Sack Theorem.
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 Overview of the Proof of the Splitting Theorem in Spaces with Non-Negative Ricci Curvature
An upper bound for a sequence of cevian inequalities.
An Upper Bound for the Minimum Diameter of Integral Point Sets.
Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten.
Andreev’s Theorem on hyperbolic polyhedra
In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that the resulting...
Another abstraction of the Erdős-Szekeres happy end theorem.
Another Space-Filling Trefoil Knot.
Answer to one of Fishburn's questions: ``Isosceles planar subsets'' [Discrete Comput. Geom. 19 (1998), no. 3, 391--398]
Our short note gives the affirmative answer to one of Fishburn’s questions.
Aperiodic Tiles.
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 isoperimetric number of strongly regular graphs.