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Harmonic diffeomorphisms and Teichmüller theory. (English) Zbl 0734.30038
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.
Reviewer: V.Oproiu (Iaşi)

30F60Teichmüller theory
30F45Conformal metrics (hyperbolic, Poincaré, distance functions)
53C21Methods of Riemannian geometry, including PDE methods; curvature restrictions (global)
58J60Relations of PDE with special manifold structures
32G15Moduli of Riemann surfaces, Teichmüller theory
Full Text: DOI EuDML
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