High-dimensional envy-free convex partition conjecture
Let n,dn,dn,d be positive integers, and let (μ11,…,μn1),…,(μ1d,…,μnd)(\mu^1_1,\dots,\mu^1_n),\dots,(\mu^d_1,\dots,\mu^d_n)(μ11,…,μn1),…,(μ1d,…,μnd) be ddd tuples of nnn absolutely continuous probability measures on Rd\mathbb{R}^dRd. A…