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arXiv · 2111.09177

Remarks on symplectic capacities of $p$-products

Pazit Haim-Kislev·Yaron Ostrover
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Abstract

In this note we study the behavior of symplectic capacities of convex domains in the classical phase space with respect to symplectic $p$-products. As an application, by using a "tensor power trick", we show that it is enough to prove the weak version of Viterbo's volume-capacity conjecture in the asymptotic regime, i.e., when the dimension is sent to infinity. In addition, we introduce a conjecture about higher-order capacities of $p$-products, and show that if it holds, then there are no non-trivial $p$-decompositions of the symplectic ball.

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Pazit Haim-Kislev, Yaron Ostrover. 2021-11-17. Remarks on symplectic capacities of $p$-products. https://doi.org/10.1142/s0129167x23500210

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