3 problems

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The sharp Lipschitz bound for Möbius transformations of the Hilbert metric in the unit ball
The conjectured Lipschitz bound. For all $x,y,a\in\mathbb{B}^n$ ,
Conjecturesolvedhilbert-metric metric-geometry unit-ball-geometryarXiv posted 2 days ago
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Sharp inclusion conjecture for triangular ratio and hyperbolic metric balls
Sharp inclusion conjecture. For $x\in G$ and $R>0$ , $B_s(x,t_0)\subseteq B_\rho(x,R)\subseteq B_s(x,t_1)$ if and only if
Conjectureopenhyperbolic-geometry metric-geometry unit-ball-geometryarXiv posted 2 days ago
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The metric conjecture for the function $w_{\mathbb{B}^n}$
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…
Conjectureopengeometric-function-theory quasi-metrics unit-ball-geometryarXiv posted 2 days ago

The sharp Lipschitz bound for Möbius transformations of the Hilbert metric in the unit ball