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Circumradius versus side lengths of triangles in linear normed spaces

Gennadiy Averkov — 2007

Colloquium Mathematicae

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 $R_{B} (T)$ the least possible radius of a Minkowskian ball enclosing T. We remark that in the terminology of location science $R_{B} (T)$ 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.

Gennadiy Averkov — 2003

Extracta Mathematicae

On area and side lengths of triangles in normed planes

Gennadiy Averkov; Horst Martini — 2009

Colloquium Mathematicae

Let $ℳ^{d}$ be a d-dimensional normed space with norm ||·|| and let B be the unit ball in $ℳ^{d}$ . Let us fix a Lebesgue measure $V_{B}$ in $ℳ^{d}$ with $V_{B} (B) = 1$ . This measure will play the role of the volume in $ℳ^{d}$ . We consider an arbitrary simplex T in $ℳ^{d}$ with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of $V_{B} (T)$ are determined. For d ≥ 3 it is noticed that the tight lower bound of $V_{B} (T)$ is zero.

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Currently displaying 1 – 6 of 6

Circumradius versus side lengths of triangles in linear normed spaces

On cross-section measures in Minkowski spaces.

On area and side lengths of triangles in normed planes

Confirmation of Matheron's conjecture on the covariogram of a planar convex body

On boundary arcs joining antipodal points of a planar convex body.

Notes on the algebra and geometry of polynomial representations.