On the orthogonal Grünbaum partition problem in dimension three

Gerardo L. Maldonado, Edgardo Roldán-Pensado

Grünbaum's equipartition problem asked if for any measure $\mu$ on ${\mathbb{R}}^d$ there are always $d$ hyperplanes which divide ${\mathbb{R}}^d$ into $2^d$ $\mu$-equal parts. This proble…