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Zeitschrift für Analysis und ihre Anwendungen


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Volume 4, Issue 4, 1985, pp. 373–383
DOI: 10.4171/ZAA/160

Published online: 1985-08-31

Konvexe Bereiche kleinster Oberfläche bei gegebener Dicke

Rolf Klötzler[1]

(1) Borsdorf, Germany

A till now unconfirmed conjecture is proved analytically: The balls are in $\mathbb E^n (n \geq 3)$ the single convex domains of given thickness with smallest surface area. The proof is effected by means of a generalized duality theory of restricted multidimensional variational problems in parametric form.

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Klötzler Rolf: Konvexe Bereiche kleinster Oberfläche bei gegebener Dicke. Z. Anal. Anwend. 4 (1985), 373-383. doi: 10.4171/ZAA/160