| A.D. Aleksandrov, Almost everywhere existence of the second dierential of a convex function and some properties of convex surfaces connected with it (in Russian), Uchenye Zapiski Leningrad. Gos. Univ., Math. Ser. 6 (1939), 3-35. |
....is the extension of f K (x) x , to a homogeneous function of degree n 1. 2000 Mathematics Subject Classification. Primary: 52A15, 52A21, 52A38. Key words and phrases. Convex body, geometric tomography, surface area measure, cosine transform, Alexandrov s theorem. A. D. Aleksandrov ([Al2]; Pog] p. 456; Sc] Corollary 2.5.3) showed that f K is the sum #(hK ) of the principal minors of order n 1 of the Hessian matrix of the support function hK . This suggests a dual version of (1) #(hK ) #) 3) which in the three dimensional case has the form: Vol 2 (K # # ) # ....
A. D. Aleksandrov, Almost everywhere existence of the second di#erential of a convex function and some properties of convex surfaces connected with it. Uchen. Zap. Leningrad. Gos. Univ. 37 Mat. 3 (1939), 3-35.
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A.D. Aleksandrov, Almost everywhere existence of the second dierential of a convex function and some properties of convex surfaces connected with it (in Russian), Uchenye Zapiski Leningrad. Gos. Univ., Math. Ser. 6 (1939), 3-35.
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