A sharp generalized Hermite-Hadamard inequality is proved and applied to obtain the optimal volume-to-central-section constant 2^n/n for symmetric projections.
Alonso-Guti\'errez, J
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On a generalization of the Hermite-Hadamard inequality and applications in convex geometry
A sharp generalized Hermite-Hadamard inequality is proved and applied to obtain the optimal volume-to-central-section constant 2^n/n for symmetric projections.