6 problems

Let $\mathbb{G}^n$ denote Gaussian space, and let $\Omega^{k+1}[\mathbb{G}^n]$ be a standard simplicial $k$-bubble, meaning a $(k+1)$-partition obtained by translating a centered s…

Let $m\geq 3$ and $0<\rho<1$. Consider two measurable partitions $\Omega_1,\ldots,\Omega_m$ and $\Omega'_1,\ldots,\Omega'_m$ of $\mathbb{R}^{n+1}$ with…

Let $me3$, and let $a_1,\dots,a_m>0$ satisfy … Let $\Omega_1,\dots,\Omega_m\subseteq\mathbb{R}^{n+1}$ be a minimizing partition for the Gaussian multi-bubble problem: the sets cover…

Let $\Omega\subseteq\mathbb{R}^{n}$ be a periodic set and let $B\subseteq\mathbb{R}^{n}$ be a periodic half space. Periodic Gaussian surface-area conjecture. The Gaussian surface a…

Let $E\subset\mathbb{R}^n$ be an open set with Lipschitz boundary and Gaussian measure $\gamma(E)=\phi(s)$, where … Its Gaussian perimeter is … and define the Gaussian isoperimetri…

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…