Author:
Hildebrandt Stefan,Tromba Anthony
Reference29 articles.
1. The classic on the isoperimetric problem is W. Blaschke, Kreis und Kugel (Berlin: W. de Gruyter, 1916; and later editions).
2. A survey on results concerning the isoperimetric problem can be found in: T. Bonnesen and W. Fenchel, Theorie der konvexen Körper (Berlin: Springer, 1934; reprinted by Chelsea Publications, New York, 1948).
3. Phenomena related to the classic isoperimetric problem were studied in the influential monograph by G. Pólya and G. Szegö, “Isoperimetric Inequalities in Mathematical Physics,” Annals of Mathematical Studies, no. 27 (Princeton University Press, 1951).
4. A typical example of a generalized isoperimetric problem is the theorem concerning which plane domain of a given area can support the largest sand pile. This result, as well as the theorem on the cross section of an elastic column with maximal torsional moment, has been proved by J. Leavitt and P. Unger, “Circle Supports of Largest Sand Pile,” Communications on Pure and Applied Mathematics 15 (1962): 35–37.
5. Experiments on capillarity are described in J. Plateau, Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires, two volumes (Paris: Gauthier-Villars, 1873).