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On the curvatures of convex bodies. (English) Zbl 0379.52004


MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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References:

[1] Aleksandrov, A.D.: Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it (Russian). Uchenye Zapiski Leningrad. Gos. Univ., Math. Ser.6, 3-35 (1939)
[2] Busemann, H., Feller, W.: Kr?mmungseigenschaften konvexer Fl?chen. Acta Math.66, 1-47 (1935) · Zbl 0012.27404 · doi:10.1007/BF02546515
[3] Gruber, P.M.: Die meisten konvexen K?rper sind glatt, aber nicht zu glatt. Math. Ann.229, 259-266 (1977) · Zbl 0349.52004 · doi:10.1007/BF01391471
[4] Klee, V.: Some new results on smoothness and rotundity in normed linear spaces. Math. Ann.139, 51-63 (1959) · Zbl 0092.11602 · doi:10.1007/BF01459822
[5] Zamfirescu, T.: The curvature of most convex surfaces vanishes almost everywhere (in preparation) · Zbl 0423.53003
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