Remarks on symplectic capacities of $p$-products

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.

21 pages

References in corpus (1)

• On symplectic capacities and their blind spots

Cited by in corpus (3)

• Symplectic polarity and Mahler's conjecture
• Quantitative Results on Symplectic Barriers
• A note on the capacities of Lagrangian $p$-sum