2 problems

Let $n$ be a positive integer, and let $\mu_1,\ldots,\mu_n$ be smooth measures in $\mathbb{R}^2$. An orthogonal path is a path formed only by horizontal and vertical segments, and…

Let $d,k\geq 1$, and let a finite measure in $\mathds{R}^d$ be bisected by a chessboard coloring if the two color classes have equal measure. Takahashi–Soberón conjecture. For any…