On boundary arcs joining antipodal points of a planar convex body.
Notes on the algebra and geometry of polynomial representations.
Circumradius versus side lengths of triangles in linear normed spaces
Given a planar convex body B centered at the origin, we denote by ℳ ²(B) the Minkowski plane (i.e., two-dimensional linear normed space) with the unit ball B. For a triangle T in ℳ ²(B) we denote by the least possible radius of a Minkowskian ball enclosing T. We remark that in the terminology of location science is the optimum of the minimax location problem with distance induced by B and vertices of T as existing facilities (see, for instance, [HM03] and the references therein). Using methods...
On cross-section measures in Minkowski spaces.
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.
Confirmation of Matheron's conjecture on the covariogram of a planar convex body
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