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A characteristic of a conformal mapping of a simply-connected domain, defined as follows: Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248001.png" /> be a simply-connected domain with more than one boundary point in the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248002.png" />-plane. Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248003.png" /> be a point of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248004.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248005.png" />, then there exists a unique function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248006.png" />, holomorphic in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248007.png" />, normalized by the conditions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248008.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c0248009.png" />, that maps <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480010.png" /> univalently onto the disc <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480011.png" />. The radius <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480012.png" /> of this disc is called the conformal radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480013.png" /> relative to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480014.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480015.png" />, then there exists a unique function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480016.png" />, holomorphic in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480017.png" /> except at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480018.png" />, that, in a neighbourhood of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480019.png" />, has a Laurent expansion of the form
+
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480020.png" /></td> </tr></table>
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and that maps <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480021.png" /> univalently onto a domain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480022.png" />. In this case the quantity <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480023.png" /> is called the conformal radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480024.png" /> relative to infinity. The conformal radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480025.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480026.png" />, relative to infinity is equal to the [[Transfinite diameter|transfinite diameter]] of the boundary <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480027.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480028.png" /> and to the [[Capacity|capacity]] of the set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480029.png" />.
+
A characteristic of a conformal mapping of a simply-connected domain, defined as follows: Let  $  D $
 +
be a simply-connected domain with more than one boundary point in the  $  z $-
 +
plane. Let  $  z _ {0} $
 +
be a point of  $  D $.  
 +
If  $  z _ {0} \neq \infty $,
 +
then there exists a unique function  $  w = f ( z) $,
 +
holomorphic in  $  D $,
 +
normalized by the conditions  $  f ( z _ {0} ) = 0 $,
 +
$  f ^ { \prime } ( z _ {0} ) = 1 $,
 +
that maps  $  D $
 +
univalently onto the disc  $  \{ {w } : {| w | < r } \} $.  
 +
The radius  $  r = r ( z _ {0} , D ) $
 +
of this disc is called the conformal radius of $  D $
 +
relative to $  z _ {0} $.  
 +
If  $  \infty \in D $,  
 +
then there exists a unique function  $  w = f ( z) $,
 +
holomorphic in  $  D $
 +
except at  $  \infty $,
 +
that, in a neighbourhood of $  \infty $,
 +
has a Laurent expansion of the form
  
An extension of the notion of the conformal radius of a domain to the case of an arbitrary domain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480030.png" /> in the complex <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480031.png" />-plane is that of the interior radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480032.png" /> relative to a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480033.png" /> (in the non-Soviet literature the term "interior radius" is used primarily in the case of a simply-connected domain). Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480034.png" /> be a domain in the complex <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480035.png" />-plane, let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480036.png" /> be a point of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480037.png" /> and suppose that a Green function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480038.png" /> for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480039.png" /> with pole at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480040.png" /> exists. Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480041.png" /> be the Robin constant of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480042.png" /> with respect to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480043.png" />, i.e.
+
$$
 +
f ( z) = z + c _ {0} + c _ {1} z  ^ {-} 1 + \dots ,
 +
$$
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480044.png" /></td> </tr></table>
+
and that maps  $  D $
 +
univalently onto a domain  $  \{ {w } : {| w | > r } \} $.
 +
In this case the quantity  $  r = r ( \infty , D ) $
 +
is called the conformal radius of  $  D $
 +
relative to infinity. The conformal radius of  $  D $,
 +
$  \infty \in D $,
 +
relative to infinity is equal to the [[Transfinite diameter|transfinite diameter]] of the boundary  $  C $
 +
of  $  D $
 +
and to the [[Capacity|capacity]] of the set  $  C $.
  
The quantity <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480045.png" /> is called the interior radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480046.png" /> relative to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480047.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480048.png" /> is a simply-connected domain whose boundary contains at least two points, then the interior radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480049.png" /> relative to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480050.png" /> is equal to the conformal radius of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480051.png" /> relative to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480052.png" />. The interior radius of a domain is non-decreasing as the domain increases: If the domains <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480053.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480054.png" /> have Green functions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480055.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480056.png" />, respectively, if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480057.png" /> and if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480058.png" />, then the following inequality holds for their interior radii <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480059.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480060.png" /> at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480061.png" />:
+
An extension of the notion of the conformal radius of a domain to the case of an arbitrary domain  $  D $
 +
in the complex  $  z $-
 +
plane is that of the interior radius of $  D $
 +
relative to a point  $  z _ {0} \in D $(
 +
in the non-Soviet literature the term  "interior radius"  is used primarily in the case of a simply-connected domain). Let  $  D $
 +
be a domain in the complex  $  z $-
 +
plane, let  $  z _ {0} $
 +
be a point of  $  D $
 +
and suppose that a Green function  $  g ( z , z _ {0} ) $
 +
for  $  D $
 +
with pole at  $  z _ {0} $
 +
exists. Let  $  \gamma $
 +
be the Robin constant of  $  D $
 +
with respect to  $  z _ {0} $,  
 +
i.e.
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480062.png" /></td> </tr></table>
+
$$
 +
\gamma  = \
 +
\left \{
 +
\begin{array}{lll}
 +
\lim\limits _ {z \rightarrow z _ {0} } [ g ( z , z _ {0} ) +  \mathop{\rm ln}  |
 +
z - z _ {0} | ]  & \textrm{ for }  &z _ {0} \neq \infty ,  \\
 +
\lim\limits _ {z \rightarrow \infty } [ g ( z , \infty ) - \mathop{\rm ln}  | z | ]  & \textrm{ for }  &z _ {0} = \infty . \\
 +
\end{array}
  
The interior radius of an arbitrary domain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480063.png" /> relative to a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480064.png" /> is defined as the least upper bound of the set of interior radii at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480065.png" /> of all domains containing <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480066.png" />, contained in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480067.png" /> and having a Green function. In accordance with this definition, if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480068.png" /> does not have a generalized Green function, then the interior radius <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480069.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480070.png" /> at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480071.png" /> is equal to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480072.png" />.
+
$$
 +
 
 +
The quantity  $  r = {e  ^  \gamma  } $
 +
is called the interior radius of  $  D $
 +
relative to  $  z _ {0} $.
 +
If  $  D $
 +
is a simply-connected domain whose boundary contains at least two points, then the interior radius of  $  D $
 +
relative to  $  z _ {0} \in D $
 +
is equal to the conformal radius of  $  D $
 +
relative to  $  z _ {0} $.
 +
The interior radius of a domain is non-decreasing as the domain increases: If the domains  $  D $,
 +
$  D _ {1} $
 +
have Green functions  $  g ( z _ {1} , z _ {0} ) $,
 +
$  g _ {1} ( z , z _ {0} ) $,
 +
respectively, if  $  z _ {0} \in D $
 +
and if  $  D \subset  D _ {1} $,
 +
then the following inequality holds for their interior radii  $  r $,
 +
$  r _ {1} $
 +
at  $  z _ {0} $:
 +
 
 +
$$
 +
r  \leq  r _ {1} .
 +
$$
 +
 
 +
The interior radius of an arbitrary domain  $  D $
 +
relative to a point $  z _ {0} \in D $
 +
is defined as the least upper bound of the set of interior radii at $  z _ {0} $
 +
of all domains containing $  z _ {0} $,  
 +
contained in $  D $
 +
and having a Green function. In accordance with this definition, if $  D $
 +
does not have a generalized Green function, then the interior radius $  r $
 +
of $  D $
 +
at $  z _ {0} \in D $
 +
is equal to $  \infty $.
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  G.M. Goluzin,  "Geometric theory of functions of a complex variable" , ''Transl. Math. Monogr.'' , '''26''' , Amer. Math. Soc.  (1969)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  V.I. Smirnov,  A.N. Lebedev,  "Functions of a complex variable" , M.I.T.  (1968)  (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  W.K. Hayman,  "Multivalent functions" , Cambridge Univ. Press  (1958)</TD></TR></table>
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  G.M. Goluzin,  "Geometric theory of functions of a complex variable" , ''Transl. Math. Monogr.'' , '''26''' , Amer. Math. Soc.  (1969)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  V.I. Smirnov,  A.N. Lebedev,  "Functions of a complex variable" , M.I.T.  (1968)  (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  W.K. Hayman,  "Multivalent functions" , Cambridge Univ. Press  (1958)</TD></TR></table>
 
 
  
 
====Comments====
 
====Comments====
In [[#References|[a2]]] the conformal radius of a compact connected set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480073.png" /> in the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480074.png" />-plane is defined as the conformal radius of its complement relative to infinity (as defined above). If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480075.png" /> is contained in a disc of radius <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480076.png" /> and has diameter <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480077.png" />, then
+
In [[#References|[a2]]] the conformal radius of a compact connected set $  E $
 +
in the $  z $-
 +
plane is defined as the conformal radius of its complement relative to infinity (as defined above). If $  E $
 +
is contained in a disc of radius $  r $
 +
and has diameter $  d \geq  r $,  
 +
then
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480078.png" /></td> </tr></table>
+
$$
 +
\rho  \leq  r  \leq  4 \rho ,
 +
$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480079.png" /> is its conformal radius (in the sense of [[#References|[a2]]], cf. [[#References|[a2]]]).
+
where $  \rho $
 +
is its conformal radius (in the sense of [[#References|[a2]]], cf. [[#References|[a2]]]).
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Tsuji,  "Potential theory in modern function theory" , Chelsea, reprint  (1975)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  P.L. Duren,  "Univalent functions" , Springer  (1983)  pp. Sect. 10.11</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Tsuji,  "Potential theory in modern function theory" , Chelsea, reprint  (1975)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  P.L. Duren,  "Univalent functions" , Springer  (1983)  pp. Sect. 10.11</TD></TR></table>

Revision as of 17:46, 4 June 2020


A characteristic of a conformal mapping of a simply-connected domain, defined as follows: Let $ D $ be a simply-connected domain with more than one boundary point in the $ z $- plane. Let $ z _ {0} $ be a point of $ D $. If $ z _ {0} \neq \infty $, then there exists a unique function $ w = f ( z) $, holomorphic in $ D $, normalized by the conditions $ f ( z _ {0} ) = 0 $, $ f ^ { \prime } ( z _ {0} ) = 1 $, that maps $ D $ univalently onto the disc $ \{ {w } : {| w | < r } \} $. The radius $ r = r ( z _ {0} , D ) $ of this disc is called the conformal radius of $ D $ relative to $ z _ {0} $. If $ \infty \in D $, then there exists a unique function $ w = f ( z) $, holomorphic in $ D $ except at $ \infty $, that, in a neighbourhood of $ \infty $, has a Laurent expansion of the form

$$ f ( z) = z + c _ {0} + c _ {1} z ^ {-} 1 + \dots , $$

and that maps $ D $ univalently onto a domain $ \{ {w } : {| w | > r } \} $. In this case the quantity $ r = r ( \infty , D ) $ is called the conformal radius of $ D $ relative to infinity. The conformal radius of $ D $, $ \infty \in D $, relative to infinity is equal to the transfinite diameter of the boundary $ C $ of $ D $ and to the capacity of the set $ C $.

An extension of the notion of the conformal radius of a domain to the case of an arbitrary domain $ D $ in the complex $ z $- plane is that of the interior radius of $ D $ relative to a point $ z _ {0} \in D $( in the non-Soviet literature the term "interior radius" is used primarily in the case of a simply-connected domain). Let $ D $ be a domain in the complex $ z $- plane, let $ z _ {0} $ be a point of $ D $ and suppose that a Green function $ g ( z , z _ {0} ) $ for $ D $ with pole at $ z _ {0} $ exists. Let $ \gamma $ be the Robin constant of $ D $ with respect to $ z _ {0} $, i.e.

$$ \gamma = \ \left \{ \begin{array}{lll} \lim\limits _ {z \rightarrow z _ {0} } [ g ( z , z _ {0} ) + \mathop{\rm ln} | z - z _ {0} | ] & \textrm{ for } &z _ {0} \neq \infty , \\ \lim\limits _ {z \rightarrow \infty } [ g ( z , \infty ) - \mathop{\rm ln} | z | ] & \textrm{ for } &z _ {0} = \infty . \\ \end{array} $$

The quantity $ r = {e ^ \gamma } $ is called the interior radius of $ D $ relative to $ z _ {0} $. If $ D $ is a simply-connected domain whose boundary contains at least two points, then the interior radius of $ D $ relative to $ z _ {0} \in D $ is equal to the conformal radius of $ D $ relative to $ z _ {0} $. The interior radius of a domain is non-decreasing as the domain increases: If the domains $ D $, $ D _ {1} $ have Green functions $ g ( z _ {1} , z _ {0} ) $, $ g _ {1} ( z , z _ {0} ) $, respectively, if $ z _ {0} \in D $ and if $ D \subset D _ {1} $, then the following inequality holds for their interior radii $ r $, $ r _ {1} $ at $ z _ {0} $:

$$ r \leq r _ {1} . $$

The interior radius of an arbitrary domain $ D $ relative to a point $ z _ {0} \in D $ is defined as the least upper bound of the set of interior radii at $ z _ {0} $ of all domains containing $ z _ {0} $, contained in $ D $ and having a Green function. In accordance with this definition, if $ D $ does not have a generalized Green function, then the interior radius $ r $ of $ D $ at $ z _ {0} \in D $ is equal to $ \infty $.

References

[1] G.M. Goluzin, "Geometric theory of functions of a complex variable" , Transl. Math. Monogr. , 26 , Amer. Math. Soc. (1969) (Translated from Russian)
[2] V.I. Smirnov, A.N. Lebedev, "Functions of a complex variable" , M.I.T. (1968) (Translated from Russian)
[3] W.K. Hayman, "Multivalent functions" , Cambridge Univ. Press (1958)

Comments

In [a2] the conformal radius of a compact connected set $ E $ in the $ z $- plane is defined as the conformal radius of its complement relative to infinity (as defined above). If $ E $ is contained in a disc of radius $ r $ and has diameter $ d \geq r $, then

$$ \rho \leq r \leq 4 \rho , $$

where $ \rho $ is its conformal radius (in the sense of [a2], cf. [a2]).

References

[a1] M. Tsuji, "Potential theory in modern function theory" , Chelsea, reprint (1975)
[a2] P.L. Duren, "Univalent functions" , Springer (1983) pp. Sect. 10.11
How to Cite This Entry:
Conformal radius of a domain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conformal_radius_of_a_domain&oldid=18740
This article was adapted from an original article by G.V. Kuz'mina (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article