Minimal surfaces, how to convert different Enneper-Weierstrass representation?
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I don't know much about Enneper-Weierstrass representation, but it seems in general, for a surface, we provide a holomorphic function $f$ and a meromorphic function $g$. For the catenoïd for instance, this would be :
$(f,g) = (-frac{e^{-z}}{2},-e^z)$. But in this documents at page 15, the author gives a representation $(G,dh)=(z,frac{1}{z})$ for the catenoïd. Are these the same? How can one in general pass from one to the other representation?
minimal-surfaces
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
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add a comment |
$begingroup$
I don't know much about Enneper-Weierstrass representation, but it seems in general, for a surface, we provide a holomorphic function $f$ and a meromorphic function $g$. For the catenoïd for instance, this would be :
$(f,g) = (-frac{e^{-z}}{2},-e^z)$. But in this documents at page 15, the author gives a representation $(G,dh)=(z,frac{1}{z})$ for the catenoïd. Are these the same? How can one in general pass from one to the other representation?
minimal-surfaces
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
$endgroup$
add a comment |
$begingroup$
I don't know much about Enneper-Weierstrass representation, but it seems in general, for a surface, we provide a holomorphic function $f$ and a meromorphic function $g$. For the catenoïd for instance, this would be :
$(f,g) = (-frac{e^{-z}}{2},-e^z)$. But in this documents at page 15, the author gives a representation $(G,dh)=(z,frac{1}{z})$ for the catenoïd. Are these the same? How can one in general pass from one to the other representation?
minimal-surfaces
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
$endgroup$
I don't know much about Enneper-Weierstrass representation, but it seems in general, for a surface, we provide a holomorphic function $f$ and a meromorphic function $g$. For the catenoïd for instance, this would be :
$(f,g) = (-frac{e^{-z}}{2},-e^z)$. But in this documents at page 15, the author gives a representation $(G,dh)=(z,frac{1}{z})$ for the catenoïd. Are these the same? How can one in general pass from one to the other representation?
minimal-surfaces
minimal-surfaces
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
asked Dec 7 '18 at 15:23
roi_saumonroi_saumon
56438
56438
add a comment |
add a comment |
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