Planning a Purely Translational Motion for a Convex Object in Two-Dimensional Space Using Generalized Voronoi Diagrams.
Polygonizations of Point Sets in the Plane.
Projections of the world onto convex polyhedra
Protecting regular polygons.
Quasi Fricke Polygons and the Nielsen Convex Region.
Räumliche Zindlerkurven.
Reconstructing Plane Sets from Projections.
Reduced spherical polygons
For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We...
Relative isodiametric inequalities.
Relative Newton Numbers.
Representation of curves of constant width in the hyperbolic plane.
Rigidity and Energy.
Rotation indices related to Poncelet’s closure theorem
Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.
Separating Convex Sets in the Plane.
Separating plane convex sets.
Separating Two Simple Polygons by a Sequence of Translations.
Sets invariant under projections onto one dimensional subspaces
The Hahn–Banach theorem implies that if is a one dimensional subspace of a t.v.s. , and is a circled convex body in , there is a continuous linear projection onto with . We determine the sets which have the property of being invariant under projections onto lines through subject to a weak boundedness type requirement.
Smoothness of vector sums of plane convex sets.
Some Extremal Results on Circles Containing Points.
Some Geometric Applications of Dilworth's Theorem.