AbstractThe packing stability in symplectic geometry was first noticed byBiran [Bir97]: the symplectic obstructions to embed several balls into amanifold disappear when their size is small enough. This phenomenonis known to hold for all closed manifolds with rational symplectic class(see [Bir99] for the 4-dimensional case, and [BH11, BH13] for higherdimensions), as well as for all ellipsoids [BH13].In this note, we show that packing stability holds for all closed, andseveral open, symplectic 4-manifolds. 1 Introduction In [Bir97, Bir99], Biran discovered the packing stability phenomenon: insome symplectic 4-manifolds, the symplectic obstructions to pack Nidenti-cal balls disappear when Nbecomes large enough. He later generalized thisresult to every closed symplectic 4-manifold with rational symplectic class([ω] ∈ H 2 (M,Q)).In this paper we generalize these results in several directions, by applyingthe singular inflation technique developed in [Ops13b, MO13]. We generalizeBiran’s packing stability to all symplectic 4-manifolds, and also to a class ofopensymplectic 4-manifolds includingellipsoids anddomainswe call pseudo-balls. For these manifolds, we establish not just packing stability but strongpacking stability, which we define now. The definition is in the spirit ofBiran’s first results on the subject [Bir97]. Throughout B(λ) will denote anopen ball of capacity λ(see Definition 1.3) and we will write U
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