7 problems

Let $\overline{\overline{\overline F}}_{c[d]}$ denote the reduced optimization expression built from the decomposition data $c[d]$, the regions $t_i$, and the convex hull…

Let $\overline F_{c[d]}$ be the asymptotic optimization quantity in the convex-hull decomposition, with local ratios $m_i/s_i$ and the function $\beta$. Constant-$\beta$ approximat…

Consider the decomposition into triangles $t_i$ indexed by $i$, with integer counts $s_i$ and $m_i$, and let $(s[d],m[d])$ maximize the quantity $f_{c[d]}$. Small-triangle occupanc…

Let $\mathbf{K}$ be a compact convex set of area $1$, let $\lambda>0$, and let $C^\star$ be the unique element of $\operatorname{argmax}\Phi_{\lambda,\mathbf{K}}$, where … Let…

Let $\mathbf{K}$ be a compact convex set in $\mathbb{R}^2$ with non-empty interior, let $\lambda>0$, and define … for compact convex sets $C\subseteq\mathbf{K}$. Write…

Consider the number of $k$-faces of the convex hull of a Poisson point process in a smooth convex body, and let the established Berry–Esseen rate for the first layer be … The $n$-t…

Let $f$ be the density and let $h$ and $\alpha$ be the functions defining the peeling layers. For $t$ fixed, set … Let $N_{n(\lambda,t),0,\lambda}$ denote the number of Poisson poi…