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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.

4 votes
2 answers
265 views

Metrics with fixed conformal structure and diameter

I have three questions. I consider a sequence of metrics $h_n$ on a two-dimensional torus which all induce the same conformal structure. Suppose that the volume of $h_n$ is always $1$. Is it possibl …
Selim G's user avatar
  • 2,696
5 votes
1 answer
462 views

Structure of the automorphism group of a Riemann surface

I was wondering if anything is known about the possible structure of $\mathrm{Aut}(S)$ for a Riemann surface $S$. More precisely, are there known obstructions for a finite group $G$ to be such an auto …
Selim G's user avatar
  • 2,696