A note on symmetrical symplectic capacities

2020/04/27 by Kun Shi, Guangcun Lu, Shi, Kun +1
Mathematics · #53C23 #53D35 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Symplectic Geometry (math.SG) #math.SG #msc:53C23 #msc:53D35

paper · pdf · doi:10.48550/arxiv.2004.12933

This note is withdrawn because there is a mistake in the proof of Theorem~1.1

openalex publication_date 2020/04/27 · arxiv created 2020/08/03 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a convex domain in the standard Euclidean symplectic space which is invariant under a linear anti-symplectic involution τ we show that its Ekeland-Hofer-Zehnder capacity is equal to the τ-symmetrical symplectic capacity of it.

Citations

• Representation formula for symmetric symplectic capacity and applications

Related

• Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities
• Asymptotic Equivalence of Symplectic Capacities
• Higher P-symmetric Ekeland-Hofer capacities
• Symplectic capacities of S¹-invariant dynamically convex domains in ℝ⁴
• Symmetrical Symplectic Capacity with Applications