On the stability of the unit circle with minimal self-perimeter in normed planes

Horst Martini, and Anatoly Shcherba. "On the stability of the unit circle with minimal self-perimeter in normed planes." Colloquium Mathematicae 131.1 (2013): 69-87. <http://eudml.org/doc/283876>.

@article{HorstMartini2013,
abstract = {We prove a stability result on the minimal self-perimeter L(B) of the unit disk B of a normed plane: if L(B) = 6 + ε for a sufficiently small ε, then there exists an affinely regular hexagon S such that S ⊂ B ⊂ (1 + 6∛ε) S.},
author = {Horst Martini, Anatoly Shcherba},
journal = {Colloquium Mathematicae},
keywords = {convex distance function; Minkowski plane; normed plane; self-perimeter; stability result},
language = {eng},
number = {1},
pages = {69-87},
title = {On the stability of the unit circle with minimal self-perimeter in normed planes},
url = {http://eudml.org/doc/283876},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Horst Martini
AU - Anatoly Shcherba
TI - On the stability of the unit circle with minimal self-perimeter in normed planes
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 1
SP - 69
EP - 87
AB - We prove a stability result on the minimal self-perimeter L(B) of the unit disk B of a normed plane: if L(B) = 6 + ε for a sufficiently small ε, then there exists an affinely regular hexagon S such that S ⊂ B ⊂ (1 + 6∛ε) S.
LA - eng
KW - convex distance function; Minkowski plane; normed plane; self-perimeter; stability result
UR - http://eudml.org/doc/283876
ER -