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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.
3
votes
Green's function - Hyperbolic Riemann surface
I would add to Mohan's response, which is correct. Even if the surface is non-compact, it might be Poincare hyperbolic but not potential theoretically hyperbolic. For example, if you take any compac …
2
votes
1
answer
215
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Uniform estimate for the Cauchy-Riemann equations on a hyperbolic Riemann surface
I have been trying to find the answer to this question in the literature, but have not succeeded. The question is as follows.
Suppose $X$ is a Riemann surface that admits a green's function (i.e. …