5 problems

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The conjecture on densest congruent geodesic ball packings in Thurston geometries
Densest-arrangement conjecture. The ball arrangement $\mathcal{B}_{\mathrm{opt}}(R_4,K_4)$ provides the densest congruent geodesic ball packing for the Thurston geometries.
Conjecturesolvedball-packings thurston-geometriesarXiv posted 2 days ago
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Horváth–Ryškov conjecture for cylinders in lattice ball packings
Consider lattice packings of the $n$ -dimensional unit ball and the largest radius of a cylinder around a line that can be inserted into the void of every such packing. Horváth–Ryšk…
Conjectureopenball-packings convex-geometry lattice-packingsarXiv posted 2 days ago
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Existence of constant-curvature ball packings from equality of extended and ordinary Yamabe invariants
Yamabe-invariant equality conjecture. If
Conjectureopenball-packings discrete-geometry yamabe-invariantarXiv posted 2 days ago
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Existence of constant-curvature ball packings under bounded vertex-degree variation
Constant-curvature packing conjecture. If
Conjectureopenball-packings discrete-geometry yamabe-flowarXiv posted 2 days ago
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Exponential lower-bound conjecture for chromatic numbers of unit ball packings
Let $\chi(d)$ denote the maximum chromatic number of the tangency graph of a unit ball packing in $d$ -dimensional Euclidean space. Exponential lower-bound conjecture. There is a co…
Conjectureopenball-packings chromatic-number strongly-regular-graphsarXiv posted 2 days ago

5 problems

The conjecture on densest congruent geodesic ball packings in Thurston geometries

Horváth–Ryškov conjecture for cylinders in lattice ball packings

Existence of constant-curvature ball packings from equality of extended and ordinary Yamabe invariants

Existence of constant-curvature ball packings under bounded vertex-degree variation

Exponential lower-bound conjecture for chromatic numbers of unit ball packings