Upper estimates on self-perimeters of unit circles for gauges

Horst Martini, and Anatoliy Shcherba. "Upper estimates on self-perimeters of unit circles for gauges." Colloquium Mathematicae 142.2 (2016): 179-210. <http://eudml.org/doc/286482>.

@article{HorstMartini2016,
abstract = {Let M² denote a Minkowski plane, i.e., an affine plane whose metric is a gauge induced by a compact convex figure B which, as a unit circle of M², is not necessarily centered at the origin. Hence the self-perimeter of B has two values depending on the orientation of measuring it. We prove that this self-perimeter of B is bounded from above by the four-fold self-diameter of B. In addition, we derive a related non-trivial result on Minkowski planes whose unit circles are quadrangles.},
author = {Horst Martini, Anatoliy Shcherba},
journal = {Colloquium Mathematicae},
keywords = {convex distance functions; gauges; Minkowski plane; normalizing figures; self-diameter; self-perimeter},
language = {eng},
number = {2},
pages = {179-210},
title = {Upper estimates on self-perimeters of unit circles for gauges},
url = {http://eudml.org/doc/286482},
volume = {142},
year = {2016},
}

TY - JOUR
AU - Horst Martini
AU - Anatoliy Shcherba
TI - Upper estimates on self-perimeters of unit circles for gauges
JO - Colloquium Mathematicae
PY - 2016
VL - 142
IS - 2
SP - 179
EP - 210
AB - Let M² denote a Minkowski plane, i.e., an affine plane whose metric is a gauge induced by a compact convex figure B which, as a unit circle of M², is not necessarily centered at the origin. Hence the self-perimeter of B has two values depending on the orientation of measuring it. We prove that this self-perimeter of B is bounded from above by the four-fold self-diameter of B. In addition, we derive a related non-trivial result on Minkowski planes whose unit circles are quadrangles.
LA - eng
KW - convex distance functions; gauges; Minkowski plane; normalizing figures; self-diameter; self-perimeter
UR - http://eudml.org/doc/286482
ER -