8 problems

Let $K\subset\mathbb{R}^n$ be a convex body, let $P>0$, and let $h(K)=\inf_{E\subset K}\operatorname{Per}(E)/|E|$ be its Cheeger constant. Higher-dimensional Cheeger log-convexity…

Let $\triangle$ be a triangle, let $\lambda_1(\triangle)$ be its first Dirichlet eigenvalue, and let … be its Cheeger constant. Parini's triangle conjecture. For any triangle…

Rathmair's conjecture. The local stability and Cheeger constants of $f$ should be finite and non-zero.

Let $\Omega\in\mathcal{K}^n$ be a convex body, let $r(\Omega)$ denote its inradius, and write $\Omega_t=\Omega\oplus tB_1$ for its parallel body. The Cheeger constant of a set $A$…

Let $\mathcal{K}^2$ denote the class of planar convex sets, and let $\omega(\Omega)$, $h(\Omega)$, and $R(\Omega)$ denote respectively the minimal width, Cheeger constant, and circ…

Let $\mathcal{K}^2$ denote the class of planar convex sets, and let $h(\Omega)$, $d(\Omega)$, and $R(\Omega)$ denote respectively the Cheeger constant, diameter, and circumradius.…

Let $\mathcal{K}^2$ denote the class of planar convex sets, and let $\omega(\Omega)$, $h(\Omega)$, and $P(\Omega)$ denote respectively the minimal width, Cheeger constant, and peri…

Let $d\geq 2$ and $p>p_c(d)$. For the giant component $\textbf{C}_n$ of supercritical bond percolation in $[-n,n]^d$, let $\Phi_{\textbf{C}_n}$ denote its Cheeger constant. Benjami…