The squeezing function on doubly-connected domains via the Loewner differential equation

For any bounded domains $\Omega$ in $\mathbb{C}^{n}$, Deng, Guan and Zhang introduced the squeezing function $S_\Omega (z)$ which is a biholomorphic invariant of bounded domains. We show that for $n=1$, the squeezing function on an annulus $A_r = \lbrace z \in \mathbb{C} : r <|z| <1 \rbrace$ is given by $S_{A_r}(z)= \max \left\lbrace |z| ,\frac{r}{|z|} \right\rbrace$ for all $0

Keywords:

• Mathematical analysis
• Bounded function
• Loewner differential equation
• Omega
• Prime (order theory)
• Mathematics
• Combinatorics
• Invariant (mathematics)

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