Kutateladze, S. S. One functional-analytical idea by Alexandrov in convex geometry. (English) Zbl 1049.52008 Vladikavkaz. Mat. Zh. 4, No. 3, 50-55 (2002). The functional-analytical approach by A. D. Alexandrov is discussed to the Minkowski and Blaschke structures making the set of convex figures into a vector space. The resultant 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. Reviewer: Victor Alexandrov (Novosibirsk) MSC: 52A40 Inequalities and extremum problems involving convexity in convex geometry 52A38 Length, area, volume and convex sets (aspects of convex geometry) 49Q20 Variational problems in a geometric measure-theoretic setting Keywords:double soap bubble; problem with current polyhedra; Blaschke-linear combination; problem with free boundary; Minkowski addition PDFBibTeX XMLCite \textit{S. S. Kutateladze}, Vladikavkaz. Mat. Zh. 4, No. 3, 50--55 (2002; Zbl 1049.52008) Full Text: EuDML