conformal injective map
$begingroup$
I have a conformal, injective map $f: Gsubset mathbb{C} rightarrow mathbb{C} $, G a domain and $D={ z in mathbb{C}: |z|leq 1} subset G $. Furthermore $z_0$ is boundary point of D with $ |f(z_0)|=max_{z in D} |f(z)|$
I want to show, that $ frac{z_0 f'(z_0)}{f(z_0)}$ is real and positive.
You have to consider, that each tangent vector of the curve $f({z:|z|=1})$ at $ f(z_0)$ is orthogonal to the direction of $ argf(z_0)$
Do I have to use that conformal maps are preserving angles, so I can consider the angle of $f^{-1}({z:|z|=1})$
Can somebody help me?
quasiconformal-maps
asked Jan 22 at 19:07
Leon1998Leon1998
549
$endgroup$
add a comment |
$begingroup$
I have a conformal, injective map $f: Gsubset mathbb{C} rightarrow mathbb{C} $, G a domain and $D={ z in mathbb{C}: |z|leq 1} subset G $. Furthermore $z_0$ is boundary point of D with $ |f(z_0)|=max_{z in D} |f(z)|$
I want to show, that $ frac{z_0 f'(z_0)}{f(z_0)}$ is real and positive.
You have to consider, that each tangent vector of the curve $f({z:|z|=1})$ at $ f(z_0)$ is orthogonal to the direction of $ argf(z_0)$
Do I have to use that conformal maps are preserving angles, so I can consider the angle of $f^{-1}({z:|z|=1})$
Can somebody help me?
quasiconformal-maps
asked Jan 22 at 19:07
Leon1998Leon1998
549
$endgroup$
add a comment |
$begingroup$
I have a conformal, injective map $f: Gsubset mathbb{C} rightarrow mathbb{C} $, G a domain and $D={ z in mathbb{C}: |z|leq 1} subset G $. Furthermore $z_0$ is boundary point of D with $ |f(z_0)|=max_{z in D} |f(z)|$
I want to show, that $ frac{z_0 f'(z_0)}{f(z_0)}$ is real and positive.
You have to consider, that each tangent vector of the curve $f({z:|z|=1})$ at $ f(z_0)$ is orthogonal to the direction of $ argf(z_0)$
Do I have to use that conformal maps are preserving angles, so I can consider the angle of $f^{-1}({z:|z|=1})$
Can somebody help me?
quasiconformal-maps
asked Jan 22 at 19:07
Leon1998Leon1998
549
$endgroup$
I have a conformal, injective map $f: Gsubset mathbb{C} rightarrow mathbb{C} $, G a domain and $D={ z in mathbb{C}: |z|leq 1} subset G $. Furthermore $z_0$ is boundary point of D with $ |f(z_0)|=max_{z in D} |f(z)|$
I want to show, that $ frac{z_0 f'(z_0)}{f(z_0)}$ is real and positive.
You have to consider, that each tangent vector of the curve $f({z:|z|=1})$ at $ f(z_0)$ is orthogonal to the direction of $ argf(z_0)$
Do I have to use that conformal maps are preserving angles, so I can consider the angle of $f^{-1}({z:|z|=1})$
Can somebody help me?
quasiconformal-maps
quasiconformal-maps
asked Jan 22 at 19:07
Leon1998Leon1998
549
asked Jan 22 at 19:07
Leon1998Leon1998
549
asked Jan 22 at 19:07
Leon1998Leon1998
549
asked Jan 22 at 19:07
Leon1998Leon1998
549
asked Jan 22 at 19:07
Leon1998Leon1998
549
549
add a comment |
add a comment |
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