Geodesic
Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 58-66

Voir la notice de l'article provenant de la source Math-Net.Ru

A convex figure $K\subset\mathbb R^2$ is a compact convex set with nonempty interior, and $\alpha K$ is a homothetic image of $K$ with coefficient $\alpha\in\mathbb R$. It is proved that for any two convex figures $K_1,K_2\subset\mathbb R^2$ there is an affine transformation $T$ of the plane such that $K_1\subset T(K_2)\subset2.7K_1$. 
@article{ZNSL_2005_329_a4,
     author = {V. V. Makeev},
     title = {Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {58--66},
     publisher = {mathdoc},
     volume = {329},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a4/}
}
TY  - JOUR
AU  - V. V. Makeev
TI  - Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 58
EP  - 66
VL  - 329
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a4/
LA  - ru
ID  - ZNSL_2005_329_a4
ER  - 
%0 Journal Article
%A V. V. Makeev
%T Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 58-66
%V 329
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a4/
%G ru
%F ZNSL_2005_329_a4
V. V. Makeev. Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 58-66. http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a4/