Geodesic
Some Characterizations of the Ellipsoid by Centroids of Concurrent Sections
Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1219-1231
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Recently M. Meyer and S. Reisner [Characterizations of ellipsoids by section-centroid location, Geometriae Dedicata 31 (1989) 345--355] proved the following result, generalizing a classical result due to Brunn [see W. Blaschke, Kreis und Kugel, Göschen Verlag, Leipzig (1916)]: If the subset K of Rn is a convex body with the property that the centroids of every set of parallel sections, cut by parallel hyperplanes, are collinear, then K is an ellipsoid.
Classification : 52A15
Mots-clés : Euclidean ball, ellipsoid, centroids 
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     author = {Z. Guerrero-Zarazua and J. Jer\'onimo-Castro and F. G. Jimenez-Lopez},
     title = {Some {Characterizations} of the {Ellipsoid} by {Centroids} of {Concurrent} {Sections}},
     journal = {Journal of convex analysis},
     pages = {1219--1231},
     year = {2020},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a7/}
}
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Z. Guerrero-Zarazua; J. Jerónimo-Castro; F. G. Jimenez-Lopez. Some Characterizations of the Ellipsoid by Centroids of Concurrent Sections. Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1219-1231. http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a7/