3 problems

Kano's conjecture. There exists a curve in $\mathds{R}^2$ formed by horizontal and vertical segments, with at most $m-1$ turns, that bisects every measure.

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…