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Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.

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Area of balls on flat surfaces

Let $S$ be a closed surface of genus $g \geq 2$. Define $\mathrm{Flat}(S)$ to be the set of marked flat metrics on $S$ with cone angles $2\pi+k\pi$ for $k\geq 0$. It is well-known that these all come …
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