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Beschreibung:
We prove some geometric inequalities for pth-order chord power integrals I_p(P_d), p=1,.,d, of d-parallelotopes P_d with positive volume V_d(P_d). First, we derive upper and lower bounds of the ratio I_p(P_d)/V_d^2(P_d) which are attained by a d-cuboid C_d with the same volume resp. the same mean breadth as P_d. Second, we apply the device of Schur-convexity to obtain bounds of I_p(C_d)/V_d^2(C_d) which are attained by a d-cube with the same volume resp. the same mean breadth as C_d. Most of these inequalities are shown for a more general class of ovoid functionals containing, as by-product, a Pfiefer-type inequality for d-parallelotopes.