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An isoperimetric partition problem. (English) Zbl 0889.52001
Let \(S_\omega\) and \(\Delta_\omega\) be the circular sector with radius 1 and angle \(\omega\in [0,2\pi]\) and the corresponding isosceles triangle, respectively. A closed set in the plane is called \(\omega\)-vector indomain if \(S_\omega \cap \Delta_\omega \subseteq B \subseteq S_\omega\) and \(\Delta_\omega \cup {\mathcal B}\) is convex.
The author analyzes the problem of finding the pair of \(\omega\)-sector indomains with fixed total perimeter length that has minimal total area and the corresponding partition of the total perimeter. After an extensive study of the analytical aspects of the problem, a computational approach is briefly discussed.

52A10 Convex sets in \(2\) dimensions (including convex curves)
52A38 Length, area, volume and convex sets (aspects of convex geometry)
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