We characterize the linear space ℋ of differences of support functions of convex bodies of 𝔼² and we consider every h ∈ ℋ as the support function of a generalized hedgehog (a rectifiable closed curve having exactly one oriented support line in each direction). The mixed area (for plane convex bodies identified with their support functions) has a symmetric bilinear extension to ℋ which can be interpreted as a mixed area for generalized hedgehogs. We study generalized hedgehogs and we extend the Minkowski inequality.
@article{bwmeta1.element.bwnjournal-article-apmv72z1p71bwm,
author = {Martinez-Maure, Yves},
title = {\'Etude des diff\'erences de corps convexes plans},
journal = {Annales Polonici Mathematici},
volume = {72},
year = {1999},
pages = {71-78},
zbl = {0952.52007},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv72z1p71bwm}
}
Martinez-Maure, Yves. Étude des différences de corps convexes plans. Annales Polonici Mathematici, Tome 72 (1999) pp. 71-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv72z1p71bwm/
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