We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
@article{bwmeta1.element.doi-10_2478_s11533-012-0129-0,
author = {Tadeusz Rze\.zuchowski},
title = {The Demyanov metric and some other metrics in the family of convex sets},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {2229-2239},
zbl = {06137113},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0129-0}
}
Tadeusz Rzeżuchowski. The Demyanov metric and some other metrics in the family of convex sets. Open Mathematics, Tome 10 (2012) pp. 2229-2239. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0129-0/
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