Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence relation. The equivalence classes form the Teichmüller space of compact Riemann surfaces of genus .
Teichmüller Space
See also
Riemann's Moduli ProblemExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Teichmüller Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TeichmuellerSpace.html