7 problems

Ramos's conjecture. The triple $(d,k,m)$ has this property whenever

Let a mass on $\mathbb{R}^d$ be a finite Borel measure that vanishes on every affine hyperplane. Steinhaus's conjecture. Any $d$ masses on $\mathbb{R}^d$ can be simultaneously bise…

Let a mass assignment in $\mathbb{R}^d$ assign continuously to each relevant linear subspace a mass distribution on that subspace, and let a $(k-1)$-horizontal linear subspace mean…

Let a mass distribution in $\mathbb{R}^d$ be a measure for which the bisection notion is defined. A set of $n$ hyperplanes bisects a mass distribution when, after orienting the hyp…

Let $R$, $B$, and $G$ be sets of lines in $\mathbb{R}^3$ in general position, each containing an even number of lines. For two lines in general position, say that one lies above th…

Barba–Pilz–Schnider conjecture. For all integers $d\geq 1$, $j\geq 1$, and $k\geq 1$, if

n-turn path conjecture. The $n+1$ measures can be split evenly using a path that has only $n$ turns.