A weighted isoperimetric inequality in a wedge

Friedemann Brock, Francesco Chiacchio, Anna Mercaldo

Let $c,k_1,...,k_N$ be non-negative numbers, and define a measure $\mu$ in the wedge $W:=\{x\in {\mathbb{R}}^N:x_i>0,i=1,...,N\}$ by $dμ= e^{c|x|^2} x_1 ^{k_1}...x_N ^{k_N}…