In this note we present inequalities relating the successive minima of an $o$-symmetric convex body and the successive inner and outer radii of the body. These inequalities join known inequalities involving only either the successive minima or the successive radii.

Keywords:

successive minima, inner and outer radii successive minima, inner and outer radii

MSC Classifications:

52A20, 52C07, 52A40, 52A39 show english descriptions Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]
Inequalities and extremum problems
Mixed volumes and related topics 52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
52C07 - Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]
52A40 - Inequalities and extremum problems
52A39 - Mixed volumes and related topics

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