5 problems

Let $f_t$ denote the density function associated with the parameter $t$, for $0\leq t\leq 1$. A density is unimodal if it is nondecreasing up to a mode and nonincreasing thereafter…

Nonexistence conjecture. The condition derived in the paper for the nonexistence of a Gerow–Robson density on $M(n)$ holds for every $n\geq 6$.

Morgan's conjecture. The isoperimetric cluster for two volumes in $\mathbf{R}^n$ with density $r^p$ is the Euclidean standard double bubble with a vertex at the origin.

Let $f_t$ denote the density function associated with the parameter $t$, for $0\leq t\leq 1$, and let $f_0$ be the right-continuous Dickman density. The supremum norm of $f_0$ is…

Let $\mathbb{H}^n$ be hyperbolic space with a smooth, radial, log-convex density, and let spheres about the origin mean geodesic spheres centered at the origin. The log-convex dens…