2 problems

Let $m>3$, let $a_1,\dots,a_m>0$ satisfy $\sum_{i=1}^m a_i=1$, and let $w\in\mathbb{R}^{n+1}$ be the vector defined in the paper. Set $\overline{w}^{(i)}=w/a_i$. Consider measurabl…

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…