10 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…

Let $\Omega$ be a bounded domain, let $\lambda_1(\Omega)$ denote its first Dirichlet eigenvalue, and define its Cheeger constant by … The Cheeger functional is…

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

Let $K$ be a planar convex body. For a direction $utheta=(costheta,sintheta)inmathbb{S}^1$, let … where $\operatorname{proj}_\theta(K)$ is the orthogonal projection onto the line…

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 $F_p$ be the functional considered in the paper on the class of admissible planar sets, and let $p=2$. A square is a candidate minimizer for the minimum of $F_2$. Square minimi…

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…