5 problems

Hadwiger's illumination conjecture for convex bodies
arXiv@arxiv
Let $n\geq 3$ and let $K$ be an $n$ -dimensional convex body. A positive homothetic copy of $K$ is a set of the form $x+\lambda K$ with $x\in\mathbb{R}^n$ and $0<\lambda<1$ . Hadwige…
Conjectureopenconvex-geometry covering illumination-problem
0
Bezdek's illumination bound for ball bodies
arXiv@arxiv
Bezdek's illumination conjecture. There exists a positive constant $\varepsilon$ such that
Conjectureopenball-bodies convex-geometry illumination-problem
0
Fractional illumination conjecture for convex bodies
arXiv@arxiv
Fractional illumination conjecture. If every affine image of $K$ is different from the hypercube $C_n$ , then
Conjectureopenconvex-geometry fractional-geometry illumination-problem
0
Levi-Hadwiger illumination conjecture
arXiv@arxiv
Levi-Hadwiger illumination conjecture. We have
Conjectureopenconvex-geometry covering-problems illumination-problem
0
Hadwiger–Boltianski illumination conjecture for convex bodies
arXiv@arxiv
For a compact set $K$ in ${\mathbb E}^n$ , a boundary point is illuminated by a direction if the corresponding half-line enters the interior of $K$ arbitrarily close to that point.…
Conjectureopenconvex-geometry illumination-problem
0

Hadwiger's illumination conjecture for convex bodies