Abstract
Let K be a convex body in \({\mathbb {R}}^n\) with ellipsoid of maximal volume \(B_2^n\). We prove that every k-dimensional central section of K has volume at most \(\frac{\left( \sqrt{k+1}\sqrt{n}\right) ^{k+1}}{k!\sqrt{k}}.\) In the centrally symmetric case the upper bound is \((\frac{4n}{k})^\frac{k}{2}.\) As an application of these inequalities we get extremal properties of cube and simplex.
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Communicated by Jean-Yves Welschinger.
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Markesinis, E. Central sections of a convex body with ellipsoid of maximal volume \(B_2^n\). Math. Ann. 378, 233–241 (2020). https://doi.org/10.1007/s00208-020-02003-7
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DOI: https://doi.org/10.1007/s00208-020-02003-7