Upper bound for the Gromov width of coadjoint orbits of type A

Abstract

We find an upper bound for the Gromov width of coadjoint orbits of U (n) with respect to the Kirillov-Kostant-Souriau symplectic form by computing certain Gromov-Witten invariants. The approach presented here is closely related to the one used by Gromov in his celebrated non-squeezing theorem.

Symplectic capacities of Hermitian symmetric spaces of compact and noncompact type

“…which, combined with (7), yields (10). To the authors' best knowledge no upper bound of c HZ (M, ω F S ) is known for HSSCT (M, ω F S ), even for the case of the complex Grassmannians (different from the projective space).…”

“…As we have already pointed out in the Introduction, inequality ( 6) is a straightforward consequence of (8) in Theorem 3. Inequality (7) follows by ( 4), by the monotonicity of c HZ and from the fact that for two compact symplectic manifolds (N 1 , ω 1 ) and (N 2 , ω 2 )…”

“…(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].…”

Minimal symplectic atlases of Hermitian symmetric spaces

“…By Darboux's theorem c G (M, ω) is a positive number or ∞. Computations and estimates of the Gromov width for various examples can be found in [2,3,4,5,7,8,10,11,14,15,16,17,18,19,21,24]. We adopt the following notation from [14].…”

Some remarks on the symplectic and Kähler geometry of toric varieties

“…Gromov width for various examples can be found in [4], [8], [17] and in particular for toric manifolds in [21].…”