For n≥3, finitely many closed standard symplectic 2n-balls of positive capacities Rᵢ embed disjointly into the interior of a ball of capacity R exactly when the sum of Rᵢⁿ is below Rⁿ and every pair satisfies Rᵢ+Rⱼ<R.
For n≥3, finitely many closed standard symplectic 2n-balls of positive capacities Rᵢ embed disjointly into the interior of a ball of capacity R exactly when the sum of Rᵢⁿ is below Rⁿ and every pair satisfies Rᵢ+Rⱼ<R.
For n≥3, finitely many closed standard symplectic 2n-balls of positive capacities Rᵢ embed disjointly into the interior of a ball of capacity R exactly when the sum of Rᵢⁿ is below Rⁿ and every pair satisfies Rᵢ+Rⱼ<R.
If correct, resolves Siegel and Yao’s high-dimensional ball-packing conjecture for arbitrary finite collections of capacities.
Are volume and two-ball constraints sufficient for symplectic ball packing in dimensions at least six?
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OpenAI reports a complete higher-dimensional symplectic ball-packing criterion
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