Geodesic
On affine diameters and chords of convex compacta
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 252-261

Voir la notice de l'article provenant de la source Math-Net.Ru

Existence theorems are proved for collections of affine diameters of a convex body that satisfy various additional conditions. The area of a convex planar figure is estimated via the maximal length of a chord dividing the area of the figure in a given ratio. 
@article{ZNSL_2003_299_a15,
     author = {V. V. Makeev},
     title = {On affine diameters and chords of convex compacta},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {252--261},
     publisher = {mathdoc},
     volume = {299},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a15/}
}
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V. V. Makeev. On affine diameters and chords of convex compacta. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 252-261. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a15/