4 problems

Let $\mathbb{R}^{n}$ be equipped with a smooth, radial, log-convex density, and consider regions of prescribed volume. Brakke's conjecture. Balls centered at the origin are isoperi…

Consider symmetric, strictly log-convex densities and perimeter-minimizing one-dimensional triple bubbles. The four types under discussion are the types labeled $2313$ and the othe…

Let $N$ and $n$ be positive integers. Consider a perimeter-minimizing $n$-bubble in $\mathbb{R}^N$ with a smooth, radially symmetric, strictly log-convex density. A standard nested…

Let $n$ be a positive integer, and let $k_1,\dots,k_m$ be positive integers satisfying … A standard nested bubble of type $(k_1,\dots,k_m)$ is a perimeter-minimizing $n$-bubble for…