Abstract
The optimal density function assigns to each symplectic toric manifold M a positive number d ≤ 1 obtained by considering the ratio between the maximum volume of M which can be filled by symplectically embedded disjoint balls and the total symplectic volume of M. In the toric version, M is toric and the balls need to be embedded respecting the toric action on M. We give a brief survey of toric symplectic manifolds and the recent constructions of moduli space structure on them, and then we recall how to define a natural density function on this moduli space. We review previous work which explains how the study of the density function can be reduced to a problem in convex geometry, and use this correspondence to to give a simple description of the regions of continuity of the maximal density function when the dimension is 4.
Communicated by: K. Strambach
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