2 problems

Eldan's robust Borell conjecture. One has $\eta\geq0$, with $\eta=0$ only when $\Omega$ is a half space, and

For $a\in(0,1)$, let $J(a,a;\rho)$ denote the Gaussian noise-stability quantity for two sets of Gaussian measure $a$, and let $\mathbb{E}_\rho J(1_A(X),1_A(Y);\rho)$ denote the cor…