Estimating Sizes of a Convex Body by Successive Diameters and Widths
نویسندگان
چکیده
The second theorem of Minkowski establishes a relation between the successive minima and the volume of a 0-symmetric convex body. Here we show corresponding inequalities for arbitrary convex bodies, where the successive minima are replaced by certain successive diameters and successive widths. We further give some applications of these results to successive radii, intrinsic volumes and the lattice point enumerator of a convex body.
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