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In this note, we show that the strong Viterbo conjecture holds true on anyconvex toric domain, and that the Viterbo's volume-capacity conjecture holdsfor the product of a $1$-unconditional convex body $A\subset\mathbb{R}^{n}$ andits polar. We also give a direct calculus proof of the symmetric Mahlerconjecture for $l_p$-balls.

The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar