A A aaaaaaaaa a a a a a a a a $\mathit{a}$ $\mathit{a}$ $\mathit{a}$ $\mathit{a}$ $\mathit{a}$ $\mathit{a}$ all all allowable alloxvable allo}νable

An an an an an an $\mathit{a}\mathrm{\text{'}}\mathit{\iota }\mathit{a}\mathit{l}\mathit{y}\mathit{t}\mathit{i}\mathit{c}$ and and and and and and are arc as as as

be be be be $\mathit{b}\mathit{c}$ belonging $\mathrm{B}{\mathrm{F}}_{\mathit{d}}\mathrm{R}\mathrm{S}$ bijecrin. bounded by by

called called $\mathrm{C}\mathit{i}\ln$ can $\mathit{c}\mathit{a}\mathrm{\prime }\mathit{\iota }\mathit{c}\mathit{a}\mathit{n}\mathit{o}\mathrm{;}\mathit{\iota }\mathit{i}\mathit{c}\mathit{a}\mathit{l}$) cell. closed closed closed closed co- compact complement

aomplex $\mathrm{C}\mathit{0}\mathit{f}\mathrm{?}{\mathit{t}}^{\mathit{J}\mathit{l}\mathit{e}\mathit{x}}$ conjectured coordinate coordinates $\mathit{c}\mathit{o}\mathit{\nu }\mathit{e}\mathit{r}\mathit{i}\mathit{n}\mathit{g}$ c $\mathrm{u}$ rve curve curves curves

define deformation deformation. denote dense distinguished distingttished distinguished

iistingttished domain

:ach each each every every $\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{I}\mathit{\gamma }$ every: $\mathit{e}\mathit{\nu }\mathit{e}\mathrm{|}\mathit{y}$

Penchel-Nielsen Fenchel-Nielsen finite finite follows t'ollows. For for for for for for form freely

genus $\mathit{g}\mathit{e}\mathit{n}\mathit{\iota }\mathrm{\ell }\mathit{s}$ genus, geodesic

has has Hausdorff have homeo- homeomorphic homotopic $\mathit{h}\mathrm{,}\mathit{v}\mathit{p}\mathit{e}\mathit{r}\mathit{p}\mathit{l}\mathit{a}\mathit{n}\mathit{e}$. $\mathit{l}\mathit{\iota }\mathit{y}\mathit{p}\mathrm{\text{'}}\mathrm{\text{'}}\mathrm{;}\mathrm{ċ}\mathit{s}\mathit{n}\mathit{r}\mathit{f}\mathit{a}\mathit{c}\mathit{e}\mathit{s}$

tdentified identificd If If if If If if, implies in in in in in induces inequality into is is is is is

ts is is is is is is is is isomorphic It

Jordan

length Let Let Let let L1PhfAN

$\mathit{m}\mathit{a}\mathrm{;}\mathit{\iota }\mathit{i}\mathit{f}\mathrm{\text{'}}\mathit{J}\mathit{l}\mathrm{\text{'}}\mathit{l}$ manifold. mapping mapping mapping $\mathit{m}\mathit{a}\mathit{p}\mathit{p}\mathit{i}\mathit{J}\mathit{\iota }\mathit{g}\mathrm{,}$ ffleet morphism Mumford)

$\mathit{O}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathrm{-}\mathrm{>}\mathit{D}\mathrm{\left(}{\mathit{S}}_{\mathrm{0}}\mathrm{\right)}\mathit{D}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathrm{\to }\mathit{D}\mathrm{\left(}{\mathit{S}}_{\mathrm{0}}\mathrm{\right)}\mathit{S}\mathrm{=}{\mathit{f}}^{\mathrm{-}\mathrm{1}}\mathrm{\left(}{\mathit{S}}_{\mathit{j}}\mathrm{\right)}\mathrm{,}$ ${\mathit{h}}_{\mathrm{*}}\mathrm{:}$ $\mathit{D}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathrm{\to }\mathit{D}\mathrm{\left(}{\mathit{S}}_{\mathrm{0}}\mathrm{\right)}\mathrm{,}$ $\mathrm{\left|}\mathrm{\right|}{\mathit{\omega }}^{\mathrm{-}\mathrm{1}}\mathrm{\left(}\mathit{c}\mathrm{\right)}\mathrm{|}\mathrm{-}\mathrm{I}\mathit{c}\mathrm{|}\mathrm{\{}\mathrm{<}\mathit{\epsilon }$.

$\mathit{C}\mathit{C}\mathit{c}\mathrm{\in }\mathit{l}\mathit{\omega }\mathit{S}\mathit{S}\mathit{S}{\mathit{c}}^{\mathrm{\prime }}\mathit{i}\mathrm{ċ}\mathit{p}$. $\mathit{p}$. ${\mathit{S}}_{\mathrm{0}}{\mathit{S}}_{\mathrm{0}}\mathit{S}\mathrm{,}$ $\mathit{S}\mathrm{,}$ $\mathit{S}$, S. ${\mathit{S}}^{\mathrm{\prime }}{\mathit{T}}_{\mathit{p}}{\mathit{T}}_{\mathit{p}}$. $\mathrm{I}\mathit{c}\mathrm{1}\mathit{c}\mathrm{\in }\mathit{C}\mathrm{.}$ $\mathit{D}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathit{D}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathit{D}\mathrm{\left(}\mathit{S}\mathrm{\right)}$

$\mathit{l}\mathrm{\left)}\mathrm{\right(}\mathit{S}\mathrm{\left)}\mathit{D}\mathrm{\right(}\mathit{S}\mathrm{\left)}\mathit{D}\mathrm{\right(}\mathit{S}\mathrm{\left)}\mathit{D}\mathrm{\right(}\mathit{S}\mathrm{)}\mathit{l}{\mathit{\chi }}_{\mathrm{t}}\mathit{\eta }\mathit{\epsilon }\mathrm{>}\mathrm{0}\mathrm{,}$ $\mathit{h}\mathrm{:}\mathit{S}\mathrm{\to }\mathit{l}\mathrm{=}\mathrm{0}\mathrm{,}$ $\mathit{l}\mathrm{>}\mathrm{0}\mathrm{,}$ ${\mathrm{C}}^{\mathrm{3}\mathit{p}\mathrm{-}\mathrm{3}}\mathit{D}{\mathrm{(}}_{\mathit{\iota }}\mathrm{S}\mathrm{)}\mathrm{,}$ $\mathrm{(}\mathit{C}\mathrm{,}\mathrm{}\mathit{\epsilon }\mathrm{)}\mathrm{(}\mathit{C}\mathrm{,}\mathrm{}\mathit{\epsilon }\mathrm{)}\mathit{\omega }\mathrm{:}{\mathit{S}}^{\mathrm{\prime }}\mathrm{\to }$

$\mathrm{\prime }\mathit{a}\mathit{e}\mathrm{\left(}{\mathit{c}}^{\mathrm{\prime }}\mathrm{\right)}$ A $\mathrm{C}\mathit{D}\mathrm{\left(}\mathit{S}\stackrel{\mathrm{`}}{\mathrm{)}}\mathrm{\right[}\mathit{f}\mathrm{]}\mathrm{\in }\mathit{A}\mathrm{,}$ $\mathrm{[}\mathit{h}\mathrm{\circ }\mathit{f}\mathrm{]}$. ${\mathrm{C}}^{\mathrm{3}\mathit{p}\mathrm{-}\mathrm{3}}$. ${\mathit{f}}^{\mathrm{-}}{}^{\mathrm{t}}\mathrm{(}\mathit{P}\mathrm{\left)}{\mathit{f}}^{\mathrm{-}\mathrm{1}}\mathrm{\right(}\mathit{S}\mathrm{\left)}\mathit{k}\mathrm{\right(}{\mathit{S}}_{\mathrm{O}}\mathrm{)}\mathrm{=}\mathit{\omega }\mathrm{:}{\mathit{S}}^{\mathrm{\prime }}\mathrm{\to }\mathit{S}\mathrm{[}\mathit{f}\mathrm{]}\mathrm{\in }{\mathit{K}}_{{\mathit{j}}^{\mathrm{\prime }}}{\mathit{f}}^{\mathrm{-}\mathrm{1}}\mathrm{(}\mathit{S}\mathrm{)}$,

${\mathit{r}}^{\mathrm{-}{\mathit{\iota }}_{\mathrm{\left(}\mathit{S}\mathrm{\right)}}}$. $\mathit{k}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathrm{+}\mathit{l}$. ${\mathit{S}}_{{\mathrm{1}}^{\mathrm{\prime }}}\mathrm{\text{...}}\mathrm{,}$ ${\mathit{S}}_{\mathit{m}}{\mathrm{b}}^{\mathrm{\prime }}\mathrm{†}\mathrm{<}\mathit{\epsilon }\mathrm{,}$ $\mathrm{\left[}\mathit{f}\mathrm{\right]}\mathrm{\in }\mathit{D}\mathrm{\left(}\mathit{S}\mathrm{\right)}\mathrm{\left[}{\mathit{f}}^{\mathrm{\circ }}\mathit{\omega }\mathrm{\right]}\mathrm{\in }\mathit{A}$. $\mathit{j}\mathrm{=}\mathrm{1}\mathrm{,}$ $\mathrm{\text{...}}$ , $\mathit{m}\mathrm{,}$ $\mathrm{\left[}\mathit{f}\mathrm{\right]}\mathrm{\in }\mathit{D}\mathrm{(}\mathit{S}\mathrm{.}\mathrm{)}$

${\mathit{K}}_{\mathit{j}}\mathrm{C}\mathit{D}\mathrm{\left(}{\mathit{S}}_{\mathit{j}}\mathrm{\right)}$,

naturally neighborhood neighborhood node node, $\mathit{J}\mathit{l}\mathrm{c}\mathrm{;}\mathit{n}\mathit{s}\dot{\mathit{\iota }}\mathrm{\prime }\mathit{l}\mathit{g}\mathit{\iota }\mathit{l}\mathrm{[}\mathit{a}\mathit{r}$ nonsingular, not not number

number,

of of of of of of of of of of of of of of of of of of of on on on on on onto onto

Dpen open ordinates

1 1220 1. 2 2. 3. 4. 51]). [1] [1, [November (and (cf. (essentially

part part parts parts point positive $\mathrm{p}$. previously proofs

rcalized Riemann ringed

same say scts set set set set small small, so-called some space space. stated $\mathrm{s}\mathrm{l}\mathrm{r}\mathit{\iota }\mathit{\iota }\mathrm{c}\mathrm{t}\mathit{\iota }\mathit{\iota }\mathrm{r}\mathrm{e}$ subset

$\mathrm{\}}\mathit{\iota }\mathrm{\neg }\mathrm{\text{'}}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{l}$, subsets subsets. such such such surfaces surfaces

Lakes takes Teichmiiller tenninal that that that that that The the the the the the $\mathit{T}\mathrm{7}\mathit{\iota }\mathit{e}$ the the

the THEORFM THEOREM THEOREM $\mathrm{T}\mathrm{H}{\mathrm{1}}^{\mathrm{\neg }}\mathrm{,}\mathrm{ċ}\mathrm{O}\mathrm{1}\mathrm{C}{\mathrm{f}}_{\mathrm{⌟}}^{\mathrm{\setminus }}\mathrm{M}$ Theorem Theorems there There $\mathit{T}\mathit{l}\mathit{\iota }\mathit{e}\mathit{r}\mathit{e}$ Thus to

to topology $\mathit{t}\mathrm{\prime }\mathrm{.}\mathit{a}\mathit{l}\mathit{\iota }\mathit{s}$" $\mathit{c}{\mathit{r}}_{\mathit{\iota }}\mathit{\sigma }\mathit{a}\mathit{l}\mathit{l}\mathit{y}$.

unique universal use

We We whenever which which which which which with with with

XV