2 problems

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Sharp distortion conjecture for the triangular ratio metric under disk Möbius transformations
Let $\mathbb{U}=\{z\in\mathbb{C}:|z|<1\}$ be the unit disk, let $0\leq a<1$ , and define the Möbius transformation … For $z_1,z_2\in\mathbb{U}$ , write $w_1=f(z_1)$ and $w_2=f(z_2)$ .…
Conjectureopenconformal-mappings moebius-transformations triangular-ratio-metricarXiv posted 2 days ago
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The conjectured exact value of the Möbius triangular-ratio Lipschitz constant
The conjectured value of $L(a)$ . For $n=2$ , numerical experiments suggest that
Conjectureopenconformal-mappings quasiconformal-maps triangular-ratio-metricarXiv posted 2 days ago

Sharp distortion conjecture for the triangular ratio metric under disk Möbius transformations