3 problems

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Fejes Tóth's hexagonal density conjecture for generalized Minkowski arrangements
Fejes Tóth's hexagonal density conjecture. For any $\mu\in(\sqrt{3}-1,1)$ and any $\mu$ -arrangement $\mathcal{F}$ in $\mathbb{R}^2$ ,
Conjecturesolveddiscrete-geometry minkowski-arrangements packing-and-coveringarXiv posted 2 days ago
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Extension of the finite-disk area bound for generalized Minkowski arrangements
Finite-disk area-bound conjecture. The displayed statement in Remark 3 holds for every $\mu$ -arrangement of finitely many disks with $\sqrt{3}-1<\mu<1$ .
Conjecturesolveddiscrete-geometry minkowski-arrangementsarXiv posted 2 days ago
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The $3^d$ conjecture for pairwise intersecting Minkowski arrangements of homothets
Let $K$ be a centrally symmetric convex body in $\mathbb{R}^d$ . A family of homothets of $K$ is a pairwise intersecting Minkowski arrangement if its members are pairwise intersecti…
Conjectureopenconvex-geometry homothets minkowski-arrangementsarXiv posted 2 days ago

Fejes Tóth's hexagonal density conjecture for generalized Minkowski arrangements