An analogue of the Krein-Milman theorem for star-shaped sets.
On curves and surfaces in illumination geometry.
Covering belt bodies by smaller homothetical copies.
On isoperimetric inequalities in Minkowski spaces.
On Reuleaux triangles in Minkowski planes.
Illumination and visibility problems in terms of closure operators.
On the chiral Archimedean solids.
A linear-time construction of Reuleaux polygons.
Unilateral tilings of the plane with squares of three sizes.
On converses of Napoleon's theorem and a modified shape function.
New extensions of Napoleon's theorem to higher dimensions.
Zum homogenen Ausleuchten konvexer Polytope
Über scharfe Schattengrenzen und Schnitte konvexer Polytope
Zur Bestimmung konvexer Polytope durch die Inhalte ihrer Projektionen
Das Volumen spezieller konvexer Polytope
Coincidences of simplex centers and related facial structures.
Zur besten Beleuchtung konvexer Polyeder
On unit balls and isoperimetrices in normed spaces
The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.
Minkowskian rhombi and squares inscribed in convex Jordan curves
We show that any convex Jordan curve in a normed plane admits an inscribed Minkowskian square. In addition we prove that no two different Minkowskian rhombi with the same direction of one diagonal can be inscribed in the same strictly convex Jordan curve.
On area and side lengths of triangles in normed planes
Let be a d-dimensional normed space with norm ||·|| and let B be the unit ball in . Let us fix a Lebesgue measure in with . This measure will play the role of the volume in . We consider an arbitrary simplex T in with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of are determined. For d ≥ 3 it is noticed that the tight lower bound of is zero.
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