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Harmonic diffeomorphisms and Teichmüller theory

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Abstract

Teichmüller spaces of Riemann surfaces usually are treated by using quasi conformal mappings. We prove the existence of a harmonic diffeomorphism between punctured surfaces. We take this to build up a Teichmüller theory and give a new proof of Teichmüller's theorem for Riemann surfaces of finite type.

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References

  • [A1] Abikoff, W.: Degenerating families of Riemann Surfaces, Ann. of Math. 105, 29–44, 1977

    Article  MathSciNet  MATH  Google Scholar 

  • [A2] Abikoff, W.: The Real Analytic Theory of Teichmüller Space, LNM 820, Springer, 1980

  • [E] Eberlein, P.: Surfaces of Nonpositive Curvature, Memoirs of AMS 218 (1979)

  • [FK] Farkas, H. and I. Kra: Riemann Surfaces, Graduate Texts in Math. 71, Springer, 1980

  • [H] Heinz, E.: Über das Nichtverschwinden der Funktionaldeterminante bei einer Klasse eineindeutiger Abbildungen, Math. Z. 105, (1968), 87–89

    Article  MathSciNet  MATH  Google Scholar 

  • [J1] Jost, J.: Two-dimensional variational problems, Vorlesungsreihe no. 6, SFB 256, Bonn

  • [J2] Jost, J.: Harmonic Maps between Surfaces, Lecture Notes in Math. 1062, Springer, 1984

  • [N] Nug, S.: The Complex Analytic Theory of Teichmüller Spaces, Canadian Math. Soc., 1988

  • [S] Sampson, J.H.: Some properties and applications of harmonic mappings, Ann. Ec. Norm. Sup. XI (1978), 211–228

    MathSciNet  MATH  Google Scholar 

  • [SY1] Schoen, R. and S.T. Yau: On Univalent Harmonic Maps between Surfaces, Invent. Math. 44 (1978), 265–278

    Article  MathSciNet  MATH  Google Scholar 

  • [SY2] Schoen, R. and S.T. Yau: Compact Group Actions and the Topology of Manifolds with Non-positive Curvature, Topology 18, (1979), 361–380

    Article  MathSciNet  MATH  Google Scholar 

  • [SY3] Schoen, R. and S.T. Yau: Harmonic Maps and the Topology of Stable Hypersurfaces and Manifolds of Non-negative Ricci curvature, Comm. Math. Helv., 51 (1976), 333–341

    Article  MathSciNet  MATH  Google Scholar 

  • [W1] Wolf, M.: The Teichmüller theory of harmonic maps, Journal of Diff. Geom. 29 (1989), 449–479

    MATH  Google Scholar 

  • [W2] Wolf, M.: Infinite Energy Harmonic Maps and Degenration of the hyperbolic Surfaces in Moduli Space, preprint

  • [Y] Yau, S.T.: A general Schwarz Lemma for Kähler Manifolds, Amer. J. Math. 100, 1, (1978), 197–203

    Article  MathSciNet  MATH  Google Scholar 

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  1. Institut für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, D-4630, Bochum

    Jochen Lohkamp

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  1. Jochen Lohkamp
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Lohkamp, J. Harmonic diffeomorphisms and Teichmüller theory. Manuscripta Math 71, 339–360 (1991). https://doi.org/10.1007/BF02568411

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  • DOI: https://doi.org/10.1007/BF02568411

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