Abstract
In the present paper, area-minimal plane convex figures with prescribed diameter and perimeter are studied. This geometrical extremal problem is a concave maximum problem. For figures with maximal circumradius it is associated with that of area-minimal sector-indomains. A corresponding perimeter partition problem is solved using methods of optimal control and nonlinear optimization. In dependence on the diameter and the perimeter a certain non-regular inpolyeder of the Reuleaux-triangle is area-minimal.
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Kripfganz, A. (1998). Isoperimetric and Isodiametric Area-minimal Plane Convex Figures. In: Schmidt, W.H., Heier, K., Bittner, L., Bulirsch, R. (eds) Variational Calculus, Optimal Control and Applications. International Series of Numerical Mathematics, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8802-8_26
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DOI: https://doi.org/10.1007/978-3-0348-8802-8_26
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