# Towards the strong Viterbo conjecture

@article{Gutt2020TowardsTS, title={Towards the strong Viterbo conjecture}, author={Jean Gutt and Vinicius G. B. Ramos}, journal={arXiv: Symplectic Geometry}, year={2020} }

This paper is a step towards the strong Viterbo conjecture on the coincidence of all symplectic capacities on convex domains. Our main result is a proof of this conjecture in dimension 4 for the classes of convex and concave toric domains. The second result is that, in any dimension, $c_{1}^{\operatorname{Ekeland-Hofer}}(W)=c_1^{CH}(W)=c_{\operatorname{Viterbo}}(W)$ for all convex domains $W\subset\mathbb{R}^{2n}$. Moreover, if $W$ is a convex or concave toric domain $W=X_\Omega\subset\mathbb{R…

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