Teichmüller's theorem

In mathematics, Teichmüller's theorem describes a fundamental result from the theory of Riemann surfaces .

It states that in every homotopy class of mappings between Riemann surfaces of the same sex there is a clear extremal, quasi-conformal map . (A quasi-conformal mapping is called extremal if the maximum of its dilation quotient is minimal among all quasi-conformal maps of the same homotopy class.)

Occasionally, Teichmüller's theorem is also used to denote the conclusion that the modular space of Riemannian surfaces of gender has the complex dimension . ${\displaystyle g}$ ${\displaystyle 3g-3}$

literature

• Oswald Teichmüller : Extremal quasi-conformal images and quadratic differentials , Prussian Academy of Sciences, nat. Kl. 22, 1–197 (1939)

Web links

• Teichmüller's Theorem (MathWorld)