On area and side lengths of triangles in normed planes

Gennadiy Averkov; Horst Martini

Colloquium Mathematicae, Tome 116 (2009), p. 101-112 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2009-01-01

Zbl 1168.52007

EUDML-ID : urn:eudml:doc:283807

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Gennadiy Averkov; Horst Martini. On area and side lengths of triangles in normed planes. Colloquium Mathematicae, Tome 116 (2009) pp. 101-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-9/