15. Variational problems in...

CI above: Variational problems in $ℝ_{2}^{n}$

15.1 The isoperimetric problem

In the Euclidean space $ℝ_{2}^{n}$ , among all compact and convex bodies with finite surface areas all equal to a given value, balls have the largest volume (p. 115 of

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Bibliography

(1) - ALEXANDROV (A.D.) - Zur Theorie der gemischten Volumina von konvexen Körpern, II: Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen, - Matematicheskii Sbornik N. S. 2, pp. 1205-1238, (en russe avec un résumé en allemand) (1937).
(2) - ANCIAUX...

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