Harmonic diffeomorphisms and Teichmüller theory (Q810673)

The author gets a global parametrization of Teichmüller spaces of noncompact Riemann surfaces of finite type. If a closed geodesic on a surface shrinks to a point then the canonical Poincaré metric on the surface converges outside the geodesic to the Poincaré metric of the limit surface. A homeomorphism between puntured surfaces is homotopic to a unique harmonic diffeomorphism of finite energy. Then the author builds up a Teichmüller theory and gives a new proof of Teichmüller's theorem for Riemann surfaces of finite type.