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Results tagged with riemann-surfaces
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user 124549
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
2
votes
1
answer
230
views
Reconstruction of Riemann surface from a germ of holomorphic function
Let $\Sigma$ be a compact Riemann surface of genus $g$, and $f: \Sigma \to \mathbb{C}$ a
meromorphic function. Take $U \subset \Sigma$ an open disk in $\Sigma$ biholomorphic to a disk
in $\mathbb{C}$, …
- 5,230
4
votes
0
answers
106
views
Elliptic integral as quantity associated with Riemann surface?
There are many elliptic integrals, so to show my point let me
just pick one of them (complete elliptic integral of the first
kind [1]):
$$K(k) = \int_{0}^{1} \frac {dx} {\sqrt{(1-x^{2})(1-k^{2}x^{2})} …
- 5,230
1
vote
1
answer
349
views
Complex structures on topological surfaces
I am interested in the number of complex structures on a surface. More precisely, given a genus $g$ surface (topological manifold of real dimension 2) with $n$ punctures $X_{(g,n)}$, how many complex …
- 91.8k