On the stability of the unit circle with minimal self-perimeter in normed planes
Volume 131 / 2013
Colloquium Mathematicum 131 (2013), 69-87
MSC: 46B20, 52A10, 52A21, 52A38.
DOI: 10.4064/cm131-1-7
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 + \varepsilon $ for a sufficiently small $\varepsilon $, then there exists an affinely regular hexagon $S$ such that $S \subset B \subset (1 + 6 \sqrt [3]{\varepsilon }) S$.
