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math.MG2020
Sections of convex bodies in John's and minimal surface area position
David Alonso-Gutiérrez, Silouanos Brazitikos
We prove several estimates for the volume, mean width, and the value of the Wills functional of sections of convex bodies in John's position, as well as for their polar bodies. The…
math.FA2020
On affine invariant and local Loomis-Whitney type inequalities
David Alonso-Gutiérrez, Julio Bernués, Silouanos Brazitikos +1
We prove various extensions of the Loomis-Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors $…
math.MG2020
Reverse Loomis-Whitney inequalities via isotropicity
David Alonso-Gutiérrez, Silouanos Brazitikos
Given a centered convex body , we study the optimal value of the constant such that there exists an orthonormal basis for whi…