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 Resource. https://mathworld.wolfram.com/TeichmuellerSpace.html