Extremal values of the integral of the mean curvature on the set of parallelepipeds with a given geodesic diameter

Rasskazova N. V.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 2.

Abstract:
In the paper, extremal values of the mean curvature integral on set of parallelepipeds with a given geodesic diameter are obtained. The maximal (minimal) value of the integral of mean curvature is attained for a degenerate parallelepiped with relation \(0:1:1\) (\(0:0:1\), respectively) for its edge lengths.

Keywords: rectangular parallelepiped, intrinsic diameter, integral of average curvature

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