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Ali Taghavi's user avatar
Ali Taghavi's user avatar
Ali Taghavi
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Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
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revised
Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
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Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
@MikhailKatz Thanks, please see the motivation I just added to the post.
revised
Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
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Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
@MikhailKatz Thanks for your comment, may be some explanation?
revised
Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
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Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
@Nicolast Must ( and Why )a holomorphic self map on torus be of finite order?Please give theorem or refrence on this and also invariance of order under deformation
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Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
asked
Is a positive degree self map on a Riemann surface homotopic to a holomorphic self map?
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Divide Euclidean space by surfaces
It is some how similar to the first part of the Hilbert 16th problem
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Holomorphic Gauss normal map
@Vik78 Thank you very much for very valuable answers of both of you which now completly solve my question.
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Holomorphic Gauss normal map
Thank you very much for this iinteresting interpretation in terms of minimal surfaces
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Holomorphic Gauss normal map
for example what can be said about pseudo sphere in space(the space image of Hyperbolic plane)?
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Holomorphic Gauss normal map
but your argument incompact case is very interesting. Thanks again for that. I admit that the non compact case is very general and wide. Howevrr I think that it is unlike that a counter example of non compact csse exist
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Holomorphic Gauss normal map
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Nonequivalent definitions in Mathematics
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Holomorphic Gauss normal map
Thank you very much for this perfect answer in compact case. Is it true that evey open Riemann surface in space admit an embedding with holomorphic Gauss map?
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Holomorphic Gauss normal map
@Vik78 yes that is very interesting question. BTW in case of identically zero curvature(cylinder)the Gauss map may fail to be holomorphic
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Holomorphic Gauss normal map
@Vik78 thank you. so the first condition we can pose is thst the curvature never vanish example sphere.
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Under what condition can a smooth map be factored through the Gauss normal map
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