Characterizing symplectic capacities on ellipsoids

2023/12/11 by Jean Gutt, Gutt, Jean, Vinicius G. B. Ramos +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2312.06476

Abstract

It is a long-standing conjecture that all symplectic capacities which are equal to the Gromov width for ellipsoids coincide on a class of convex domains in ℝ²ⁿ. It is known that they coincide for monotone toric domains in all dimensions. In this paper, we study whether requiring a capacity to be equal to the k^th Ekeland-Hofer capacity for all ellipsoids can characterize it on a class of domains. We prove that for k=n=2, this holds for convex toric domains, but not for all monotone toric domains. We also prove that for k=n≥ 3, this does not hold even for convex toric domains.

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