Optimal constants in normed planes

V. Balestro, H. Martini and R. Teixeira, Optimal constants in normed planes, Journal of Convex Analysis 26(1), pp. 89-104, 2019. (arXiv link) (journal link)

Comments: Some new constants in normed planes are studied, and some calculations of new and old constants for certain classes of normed planes are made. One of the new constants is related, at least in the Radon case, to the following (still open, as far as I know) problem posed by Marek Lassak: what are the centrally symmetric closed convex curves whose every inscribed affine regular hexagons have the same area? A special emphasis is given to characterize the geometry of the planes for which extremal values are attained.