Solution of the propeller conjecture in ${\mathbb{R}}^3$

Steven Heilman, Aukosh Jagannath, Assaf Naor

It is shown that every measurable partition $A_1,...,A_k$ of ${\mathbb{R}}^3$ satisfies $$\sum _{i=1}^k||{\int }_{A_i}x{e}^{-\frac{1}{2}||x|{|}_2^2}dx|{|}_2^2\le 9{\pi }^2.(\ast )$$ Let ${P_1,P_2…