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Results tagged with riemann-surfaces
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user 1162
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
1
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3
answers
727
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A special case of the uniformization theorem
I am interested in a proof of the following fact :
Suppose that $X$ is a Riemann surface homeomorphic to the Riemann sphere. Then $X$ is conformally equivalent to the Riemann sphere.
Of course, this …
- 2,154
9
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3
answers
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Can the limit set of an infinitely generated Schottky group have positive area?
Dear Mathoverflow Community,
Suppose that $\Omega$ is a domain in the Riemann Sphere $\widehat{\mathbb{C}}$ with $\infty \in \Omega$, and assume that every connected component of $\partial \Omega$ is …
- 2,154
4
votes
A question on Ahlfors covering surface
Yes it can, see the paper A new proof of the Ahlfors five islands theorem by Walter Bergweiler. The proof is based on a result on Nevanlinna concerning perfectly branched values, Zalcman's rescaling l …
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8
votes
Accepted
Fixed points on Riemann surface
This theorem is an immediate consequence of a result by B. Maskit, which states that one may associate with $\Omega$ another domain $\Omega'$, conformally equivalent to $\Omega$, such that all conform …
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3
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Reference request: uniformization theorem
Let me second Alex Eremenko's suggestion for
Donald Marshall, Complex Analysis, Cambridge 2019.
The proof is based on the new notion of dipole Green's function, and is especially interesting in view o …
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