3 problems

The constant-width illumination conjecture in three dimensions
Let $\mathbf{K}$ be a three-dimensional convex body of constant width. Constant-width illumination conjecture. The illumination number satisfies $I(\mathbf{K})=4$ . The known genera…
openFrom papersconstant-width-bodies convex-geometry illumination
0 responses
3
Translative equal-volume property and Euclidean constant width
Translative constant-width conjecture. If $d\geq3$ and some $K\in\mathcal{K}_d$ satisfies the translative equal volume property, then $K$ is a convex body of constant width in a Eu…
openFrom papersconstant-width-bodies convex-geometry normed-spaces
0 responses
3
Ellipsoid characterization from the translative constant volume property
Translative constant volume conjecture. Then $K$ is an ellipsoid.
openFrom papersconstant-width-bodies convex-geometry
0 responses
9

The constant-width illumination conjecture in three dimensions