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
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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},
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 -
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/