Symplectic Ball Packings in Higher Dimensions
We prove that, for all integers n ≥ 3 and k ≥ 1 and all positive real capacities $R_1,\ldots,R_k$, the closed standard symplectic $2n$-balls of these capacities embed disjointly into the interior of a ball of capacity R > 0 if and only if $\displaystyle \sum_{i=1}^k R_i^n\lt R^n, \qquad R_i+R_j\lt R\quad(i\ne j).$ Capacity is π times the squared Euclidean radius, and each embedding is defined on a neighborhood of its closed source ball. This proves Siegel and Yao's Conjecture A.
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