Remarks on symplectic capacities of p-products

Pazit Haim-Kislev*, Yaron Ostrover

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, 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 nontrivial p-decompositions of the symplectic ball.

Original languageEnglish
Article number2350021
JournalInternational Journal of Mathematics
Volume34
Issue number4
DOIs
StatePublished - 1 Mar 2023

Keywords

  • Symplectic capacities
  • Viterbo's volume-capacity conjecture
  • p-products

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