Geodesic
The Kuperberg conjecture for translates of convex bodies
Roman Prosanov1 ; Roman Prosanov
1Université de Fribourg, Fribourg, Switzerland; Moscow Institute of Physics And Technology, Dolgoprudny, Russia
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1017-1021 
Roman Prosanov; Roman Prosanov. The Kuperberg conjecture for translates of convex bodies. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1017-1021. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a102/
@article{AMUC_2019_88_3_a102,
     author = {Roman Prosanov and Roman Prosanov},
     title = { The {Kuperberg} conjecture for translates of convex bodies},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {1017--1021},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a102/}
}
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Voir la notice de l'article provenant de la source Comenius University

We prove that if a convex body $C$ admits a dense translative packing, then it admits an economical translative covering and vice versa. This answers positively to the question of W. Kuperberg in the case of translative arrangements.