Symplectic capacities of classical domains

Abstract

Abstract. In this note we calculate Gromov symplectic width and HoferZehnder symplectic capacity for the classical domains.Mathematics Subject Classification: 53D35, 57R17, 53D05

Symplectic capacities of Hermitian symmetric spaces of compact and noncompact type

“…The proof of Theorem 4 which extends the results in [35] valid for classical Cartan domains to the product of Cartan domains (including the exceptional ones), is based (together with the inclusion B 2n (1) ⊂ (Ω, ω 0 )) on the fact that any n-dimensional Cartan domain (Ω, ω 0 ) symplectically embeds into the cylinder (Z 2n (1), ω 0 ) (see Sections 4 and 5 for details).…”

“…Remark 13. The inclusion (31) has been obtained in [ [35] for the case of classical Cartan domains). Combining this with the symplectic embedding (29) Lu was able see [34,Theorem 1.35] to obtain the upper bound…”

“…Remark 14. A similar (symplectic) embedding (Ω, ω 0 ) ֒→ (Z 2n (1), ω 0 ) has been considered in [35] for the classical Cartan domains. (27)).…”

“…Remark 13. The inclusion (31) has been obtained in [34,Lemma 4.2,Section 4] for the case of the first Cartan domain, namely B 2k(n−k) (1) ⊂ Ω I [k, n] (see also [35] for the case of classical Cartan domains). Combining this with the symplectic embedding ( 29) Lu was able see [34,Theorem 1.35] to obtain the upper bound…”

“…(2) By Darboux's theorem c G (M, ω) is a positive number. Computations and estimates of the Gromov width for various examples can be found in [3], [4], [5], [7], [17], [18], [23], [28], [34], [35], [36], [37], [45], [50].…”