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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 …
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2 votes
1 answer
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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. …
Dror's user avatar
  • 174