Geodesic
Large Curvature on Typical Convex Surfaces
Journal of convex analysis, Tome 19 (2012) no. 2, pp. 385-391.

Voir la notice de l'article provenant de la source Heldermann Verlag

We show in this paper that on most convex surfaces there exist points with arbitrarily large lower curvature in every tangent direction. Moreover, we show that, astonishingly, on most convex surfaces, although the set of points with curvature 0 in every tangent direction has full measure, it contains no pair of opposite points, i.e. points admitting parallel supporting planes. 
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     author = {K. Adiprasito and T. Zamfirescu},
     title = {Large {Curvature} on {Typical} {Convex} {Surfaces}},
     journal = {Journal of convex analysis},
     pages = {385--391},
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     number = {2},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a3/}
}
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K. Adiprasito; T. Zamfirescu. Large Curvature on Typical Convex Surfaces. Journal of convex analysis, Tome 19 (2012) no. 2, pp. 385-391. http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a3/