The following is the list of corrections to be added to any subsequent edition of the book.
Page xvii, line 6, the second to last bullet. Contrary to what is stated at the beginning of this paragraph on the previous page, the book does not contain the proof that the Teichmuller space of a closed subset of the Riemann sphere is a complex manifold universal for holomorphic motions of a closed set. The first result of this type is proved in G. Leib's thesis, referenced in the bibliography. The infinitesimal foundation for the theory of the Teichmuller space of a closed set is developed in Chapter 3 and its appendix.
Page 31, remark to Proposition 3. It is true that Slodkowski's extension theorem for the case of a closed subset of the Riemann sphere consisting of four points is equivalent to Agard's formula. However, the proof of the reverse implication not given in the remark requires the use of Teichmuller's existence and uniqueness theorem for the Teichmuller space of a four-times punctured sphere. In this remark, a reference should have been made to the paper by Irwin Kra cited below.
page 83, line 7, change "a" with "an".
It
should be "by an isotopy that..."
page 86, line -10, insert the period "."
It should say
"...geodesics. The property that horizontal..."
page 87, line 15, add the right ")".
It should be
$...([x_{i-1},x_i])$ is contained ..."
page 88, line -9,
change 'Figure 4.1a" to "Figure 4.2a"
and "\varphi" into "\tilde{varphi}".
It should be
"...vertices of Figure
4.2a is
$\pi$ and the total change in $arg \tilde{\varphi}$ at ..."
Also, in
the following two displayed formulas (lines -6 and
-8 on the same page) change "
in Figure 4.1a"
to "Figure 4.2a" and "Figure 4.1b" to "Figure
4.2b".
page 94, line -13, change "an" to "a".
It
should be "...identity through a homotopy fixing..."
Also on the same page, line 10, delete the word "\varphi".
It
should be "integrable, holomorphic, quadratic differential..."
page 103, line 2, delete the word "are" from "are
are". It should be "...coefficient are are simultaneously
small."
page 127, line 5, change "formulae" to "
formulas".
It should be " ...consequence of these formulas is that,..."
page 130, line -16, delete the right ")"
from the statement of
Lemma 2. It should be" Lemma 2
(Thurston) Suppose $f$
is...."
page 155, line 2, change"..from T(R_1) onto T(R)" to " from T(R) onto T(R_1)"
Also, on same page, line -10, change" Then F=\rho_g \circ G..." to " Then F= G \circ \rho_g is a biholomorphic map fixing basepoints, that is,...$quot;
Also, on the same page, line -4, change"..of R onto R^{\mu}" to "of R^{\mu} onto R"
page 157, line 1, add "in". It should say "By arguments given in Chapter 11..."
page 178, line -7, the following should be added: This chapter has been based mostly on [*].
* V. Bozin, N. Lakic, M. Markovic and M. Mateljevic, Unique extremality, Jornal D'Analyse 75(1998) (see Bibliography)
page 230, line -14, change "\lambda_z" to "\lambda
z". It should be "...transformation $A(z)=\lambda z.$
Thus, a power..."
page 235, line -14, insert the words "
have been developed".
It should be "Further properties of the heights mapping have
been developed
in..."
page 238, change (...) with the absolute value symbols
"|...|$ in the
numerator in formula (12.13). Also, on the same page, add
the right absolute value symbol "|" in the numerators
on lines
-3 and -11. It should be "
...\frac{|1-\mu(\varphi/|\varphi|)|^2}{...$
at both places.
page 239, line 12, change "mapping" to "
mappings".
It should be "From the theory of quasiconformal mappings
$f^....."
Also, on same page, line -6, add the blank line between the words
"n"
an "integers".
page 240, line -13, change "\theta" to "
\theta_1.$ It
should be "...quadratic differentials $e^{2i\theta_1}dz^2$ and
$e^{2i\theta_2}dz^2$ with..."
page 337, line -6, change the sentence which begins
"We call points..." to "
We call points $a$ and $b$ of $S$ adjacent if they are the endpoints
of an interval of the circle that contains no other points of $S.$
"
The following references should be added to the bibliography:
V. Bozin, N. Lakic, M. Markovic and M. Mateljevic, Unique extremality, J. D'Analyse 75(1998), 299-338.
I. Kra, On Teichmuller's theorem on the quasi-invariance of cross-ratios, Israel J. of Math. 30(1978), 152-158.
S. Nag, The Complex Analytic Theory of Teichmuller Spaces, Can. Math. Soc. series of Monographs, Wiley-Interscience(1988).
The reference [Tan92b] on page 366 should be changed to [IT92] Y. Imayoshi and M. Taniguchi, An introduction to Teichmuller space, Springler-Verlag, Tokyo, 1992.