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

@article{Shi2020TheVC, title={The Viterbo's capacity conjectures for convex toric domains and the product of a \$1\$-unconditional convex body and its polar}, author={Kun Shi and Guangcun Lu}, journal={arXiv: Symplectic Geometry}, year={2020} }

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

## One Citation

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