2 problems

Higher-dimensional double-bubble classification conjecture. A perimeter-minimizing double bubble is either

Let $(M^n,g,v,m,0)$ be a closed weighted Einstein manifold with $P_\phi^m=\lambda g>0$ and scale $\kappa>0$. Let $I_1,I_2\colon C^\infty(M)\to\mathbb{R}$ be the functionals defined…