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

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.