5 problems

Quasi-metric inequality conjecture. In this setting, the inequality holds, with the obvious modifications, for bounded Lipschitz domains $\Omega$ and operators $L$ with bounded mea…

Sharp quasi-metric constant conjecture. For every $\alpha>0$, $p^\alpha_{\mathbb{B}^n}$ is a quasi-metric with sharp constant $c_*(\alpha)$. Equivalently, $c_*(\alpha)$ is the best…

Let $\mathbb{B}^2$ be the unit disk, and let $s_{\mathbb{B}^2}$ and $w_{\mathbb{B}^2}$ denote the triangular ratio metric and the function defined in the paper, respectively. The s…

Let $\mathbb{B}^n$ be the unit ball in $\mathbb{R}^n$. For $x,y\in\mathbb{B}^n\setminus\{0\}$, define $\widetilde{x}=x(2-|x|)/|x|$ and $\widetilde{y}=y(2-|y|)/|y|$, and set … Also…

Let $G errbracketmathbb{R}^n$ be a domain, and let $pG$ denote the point pair function. A function $d$ is a quasi-metric if there is a constant $cgeq 1$ such that…