JournalscmhVol. 91, No. 1pp. 131–144

Asymptotic equivalence of symplectic capacities

  • Efim D. Gluskin

    Tel Aviv University, Israel
  • Yaron Ostrover

    Tel Aviv University, Israel
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Abstract

A long-standing conjecture states that all normalized symplectic capacities coincide on the class of convex subsets of R2n\mathbb R^{2n}. In this note we focus on an asymptotic (in the dimension) version of this conjecture, and show that when restricted to the class of centrally symmetric convex bodies in R2n\mathbb R^{2n}, several symplectic capacities, including the Ekeland–Hofer–Zehnder capacity, the displacement energy capacity, and the cylindrical capacity, are all equivalent up to a universal constant.

Cite this article

Efim D. Gluskin, Yaron Ostrover, Asymptotic equivalence of symplectic capacities. Comment. Math. Helv. 91 (2016), no. 1, pp. 131–144

DOI 10.4171/CMH/380