On area and side lengths of triangles in normed planes

Gennadiy Averkov, and Horst Martini. "On area and side lengths of triangles in normed planes." Colloquium Mathematicae 115.1 (2009): 101-112. <http://eudml.org/doc/283807>.

@article{GennadiyAverkov2009,
abstract = {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.},
author = {Gennadiy Averkov, Horst Martini},
journal = {Colloquium Mathematicae},
keywords = {area; geometric inequality; complete systems of inequalities; metric space; normed space; Minkowski space; Santaló diagram; simplex; triangle},
language = {eng},
number = {1},
pages = {101-112},
title = {On area and side lengths of triangles in normed planes},
url = {http://eudml.org/doc/283807},
volume = {115},
year = {2009},
}

TY - JOUR
AU - Gennadiy Averkov
AU - Horst Martini
TI - On area and side lengths of triangles in normed planes
JO - Colloquium Mathematicae
PY - 2009
VL - 115
IS - 1
SP - 101
EP - 112
AB - 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.
LA - eng
KW - area; geometric inequality; complete systems of inequalities; metric space; normed space; Minkowski space; Santaló diagram; simplex; triangle
UR - http://eudml.org/doc/283807
ER -