The Gromov width of 4-dimensional tori

Abstract

We show that every 4-dimensional torus with a linear symplectic form can be fully filled by one symplectic ball. If such a torus is not symplectomorphic to a product of 2-dimensional tori with equal sized factors, then it can also be fully filled by any finite collection of balls provided only that their total volume is less than that of the 4-torus with its given linear symplectic form.

improved exposition, proof of Proposition 3.9 clarified, discussion of ellipsoid embeddings removed

Cited by in corpus (10)

• Mahler's conjecture for some hyperplane sections
• Equality cases in Viterbo's conjecture and isoperimetric billiard inequalities
• Unobstructed symplectic packing for tori and hyperkahler manifolds
• The Gromov width of coadjoint orbits of the symplectic group
• The Gromov width of generalized Bott manifolds
• Minimal symplectic atlases of Hermitian symmetric spaces
• Symplectic geometry of Cartan-Hartogs domains
• The Gromov width of Bott-Samelson varieties
• Newton-Okoukov bodies and symplectic embeddings into non-toric rational surfaces
• From Lagrangian Products to Toric Domains via the Toda Lattice