2011/04/18 by Olguţa Buşe, Buse, Olguta, Martin Pinsonnault +1
Computer Science · Mathematics · #53D05 #57R17 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1104.3362
openalex publication_date 2011/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic 4-manifolds. We give explicit formulae for the packing numbers, the generalized Gromov widths, the stability numbers, and the corresponding obstructing exceptional classes. As a corollary, we give explicit values for when an ellipsoid of type E(a, b), with (b)/(a) ∈ \N, embeds in a polydisc P(s,t). Under this integrality assumption, we also give an alternative proof of a recent result of M. Hutchings showing that the ECH capacities give sharp inequalities for embedding ellipsoids into polydisks.