Errata \( \newcommand{\ds}{\displaystyle} \newcommand{\diam}{\operatorname{diam}} \newcommand{\area}{\operatorname{area}} \newcommand{\dist}{\operatorname{dist}} \newcommand{\ord}{\operatorname{ord}} \newcommand{\res}{\operatorname{res}} \newcommand{\wind}{\operatorname{W}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\SL}{\operatorname{SL}} \newcommand{\PSL}{\operatorname{PSL}} \newcommand{\iso}{\stackrel{\cong}{\longrightarrow}} \newcommand{\myint}{\operatorname{int}} \newcommand{\ve}{\varepsilon} \newcommand{\es}{\emptyset} \newcommand{\sm}{\smallsetminus} \newcommand{\bd}{\partial} \newcommand{\Chat}{\hat{\mathbb C}} \newcommand{\Cstar}{{\mathbb C}^*} \newcommand{\Dstar}{{\mathbb D}^*} \newcommand{\myre}{\operatorname{Re}} \newcommand{\myim}{\operatorname{Im}} \newcommand{\ov}{\overline} \newcommand{\io}{\iota} \newcommand{\con}{\operatorname{const.}} \newcommand{\OO}{{\mathcal O}} \newcommand{\MM}{{\mathcal M}} \newcommand{\FF}{{\mathcal F}} \newcommand{\CC}{{\mathbb C}} \newcommand{\PP}{{\mathbb P}} \newcommand{\RR}{{\mathbb R}} \newcommand{\HH}{{\mathbb H}} \newcommand{\TT}{{\mathbb T}} \newcommand{\II}{{\mathbb I}} \newcommand{\ZZ}{{\mathbb Z}} \newcommand{\NN}{{\mathbb N}} \newcommand{\DD}{{\mathbb D}} \newcommand{\QQ}{{\mathbb Q}} \)




Errata

Last update: 12/23/2021

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  • Page 51, proof of Corollary 2.18: As a clarification, observe that $s \mapsto \tilde{H}(0,s)$ is constant since it is a continuous map taking values in the totally disconnected set $\exp^{-1}(\gamma_0(0))$. Since $\tilde{H}(0,0)=p$, it follows that $\tilde{H}(0,s)=p$ for all $s$.
  • Page 139, Theorem 5.8: The very end of the proof is a bit too fast because $X$ is not assumed complete, so Cauchy sequences in $X$ are not guaranteed to converge. However, using condition (i) we know that for every $p \in K$ the Cauchy sequence $\{ f_n(p) \}_{n \in S}$ has a convergent subsequence and therefore must converge. Clearly the convergence is uniform on $K$.
  • Page 155, Problem 8: Change “Hurwitz's Theorem 5.18” to “Lemma 5.16.”
  • Page 166, second paragraph of the proof of Corollary 6.9: If $|b_1|=1$, then $b_n=0$ for all $n \geq 2$ so $\psi(w)=b_0+\alpha Z(\alpha^{-1} w)$ where $\alpha$ a square root of $b_1$. Conversely, if this relation holds for some $\alpha$ with $|\alpha|=1$, then $|b_1|=|\alpha^2|=1$.
  • Page 167, line $-$8: Change “Laurant” to “Laurent.”
  • Pages 349, 351, 353, 355: The running heads misspell “Ahlfors” as “Alfors.”