On area and side lengths of triangles in normed planes

• Autorzy: Gennadiy Averkov , Horst Martini
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 52A10: Convex sets in 2 dimensions (including convex curves)
• 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
• 52B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 115
• Numer: 1
• Strony: 101-112

Daty

wydano

2009

Twórcy

autor

Gennadiy Averkov

• Faculty of Mathematics, University of Magdeburg, 39106 Magdeburg, Germany

autor

Horst Martini

• Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany

Identyfikatory

DOI

10.4064/cm115-1-9