Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 58-66
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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/
@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},
year = {2005},
volume = {329},
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
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
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a4/
%G ru
%F ZNSL_2005_329_a4
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 $K_1\subset T(K_2)\subset2.7K_1$.
