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Remarks on symplectic capacities of p-products

Pazit Haim-Kislev

School of Mathematical Sciences, Tel Aviv University, Israel

E-mail Address: pazithaim@mail.tau.ac.il

Corresponding author.

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and

Yaron Ostrover

https://orcid.org/0000-0002-7981-8619

School of Mathematical Sciences, Tel Aviv University, Israel

E-mail Address: ostrover@tauex.tau.ac.il

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https://doi.org/10.1142/S0129167X23500210Cited by:3 (Source: Crossref)

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.

Communicated by Paul Biran

Keywords:

AMSC: 53D05, 52A20, 52A40

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