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Isoperimetric and Isodiametric Area-minimal Plane Convex Figures

  • Anita Kripfganz
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)

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.

Keywords

Convex Body Partition Problem Central Angle Plane Convex Perimeter Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Anita Kripfganz
    • 1
  1. 1.Institut für MathematikUniversität LeipzigLeipzigGermany

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