Geodesic
One functional-analytical idea by Alexandrov in convex geometry
Vladikavkazskij matematičeskij žurnal, Tome 4 (2002) no. 3, pp. 50-55 Cet article a éte moissonné depuis la source Math-Net.Ru

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The functional-analytical approach by A. D. Alexandrov is discussed to the Minkowski and Blaschke structures making the set of convex compact figures into a vector space. The resulting analytical possibilities are illustrated by the isoperimetric type problems of finding convex figures separated by current hyperplanes similar to the Urysohn and double bubble problems. 
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S. S. Kutateladze. One functional-analytical idea by Alexandrov in convex geometry. Vladikavkazskij matematičeskij žurnal, Tome 4 (2002) no. 3, pp. 50-55. http://geodesic.mathdoc.fr/item/VMJ_2002_4_3_a5/

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[7] Kutateladze S. S., “On the isoperimetric type problems with current hyperplanes”, Sibirsk. Mat. Zh., 43:4 (2002), 811–815 (to appear) (in Russian) | MR | Zbl