2 problems

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Bonnesen–Fenchel conjecture on minimum-volume bodies of constant width in three dimensions
Let $\mathbb{E}^3$ be three-dimensional Euclidean space, and consider convex bodies of constant width $2$ in $\mathbb{E}^3$ . Bonnesen–Fenchel conjecture. Meissner's bodies are the…
Conjectureopenbodies-of-constant-width convex-geometryarXiv posted 3 days ago
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Danzer's simplex-symmetry conjecture for minimum-volume bodies of constant width
Let a body of constant width be a convex body in Euclidean space, and let its symmetry group be the group of Euclidean symmetries preserving the body. A regular simplex is a regula…
Conjectureopenbodies-of-constant-width convex-geometry symmetryarXiv posted 3 days ago

Bonnesen–Fenchel conjecture on minimum-volume bodies of constant width in three dimensions