Geodesic
One functional-analytical idea by Alexandrov in convex geometry
Vladikavkazskij matematičeskij žurnal, Tome 4 (2002) no. 3, pp. 50-55

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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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     author = {S. S. Kutateladze},
     title = {One functional-analytical idea by {Alexandrov} in convex geometry},
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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/