Commentarii Mathematici Helvetici

, Volume 70, Issue 1, pp 659–673 | Cite as

Convex functionals and generalized harmonic maps into spaces of non positive curvature

  • Jürgen Jost
Article

Keywords

Riemannian Manifold Lower Semicontinuous Isometry Group Positive Curvature Nonpositive Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A1]Al'ber, S. I.,On n-dimensional problems in the calculus of variations in the large, Sov. Math. Dokl.5 (1964), 700–804.Google Scholar
  2. [A2]Al'ber, S. I.,Spaces of mappings into a manifold with negative curvature, Sov. Math. Dokl.9 (1967), 6–9.Google Scholar
  3. [At]Attouch, H.,Variational convergence for functions and operators, Pitman, 1984.Google Scholar
  4. [C1]Corlette, K.,Flat G-Bundles with canonical metrics, J. Diff. Geom.28 (1988), 361–382.MathSciNetGoogle Scholar
  5. [C2]Corlette, K.,Archimedean superrigidity and hyperbolic geometry, Ann. Math.135 (1992), 165–182.CrossRefMathSciNetGoogle Scholar
  6. [D]Donaldson, S.,Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc.55 (1987), 127–131.MathSciNetGoogle Scholar
  7. [dM]dal Maso, G.,An introduction to Γ-convergence, Birkhäuser, 1993.Google Scholar
  8. [DO]Diederich, K. andOhsawa, T.,Harmonic mappings and disk bundles over compact Kähler manifolds, Publ. Res. Inst. Math. Sci.21 (1985), 819–833.MathSciNetGoogle Scholar
  9. [ES]Eells, J. andSampson, J.,Harmonic mappings of Riemannian manifolds, Am. J. Math.85 (1964), 109–160.CrossRefMathSciNetGoogle Scholar
  10. [GS]Gromov, M. andSchoen, R.,Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. Math. IHES76 (1992), 165–246.MathSciNetGoogle Scholar
  11. [H]Hartman, P.,On homotopic harmonic maps, Can. J. Math.19 (1967), 673–687.MathSciNetGoogle Scholar
  12. [J]Jost, J.,Equilibrium maps between metric spaces, Calc. Var.2 (1994), 173–204.CrossRefMathSciNetGoogle Scholar
  13. [JY1]Jost, J. andYau, S. T.,The strong rigidity of locally symmetric complex manifolds of rank one and finite volume, Math. Ann.271 (1985), 143–152.CrossRefMathSciNetGoogle Scholar
  14. [JY2]Jost, J. andYau, S. T.,On the rigidity of certain discrete groups and algebraic varieties, Math. Ann.278, (1987) 481–496.CrossRefMathSciNetGoogle Scholar
  15. [JY3]Jost, J. andYau, S. T.,Harmonic maps and group representations, in: B. Lawson and K. Tenenblat (eds.),Differential Geometry and Minimal Submanifolds, Longman Scientific, 1991, pp. 241–260.Google Scholar
  16. [JY4]Jost, J. andYau, S. T.,Harmonic maps and superrigidity, Proc. Sym. Pure Math.54, Part I (1993), 245–280.MathSciNetGoogle Scholar
  17. [JZ1]Jost, J. andZuo, K., Harmonic maps andSl(r,ℂ)-representations ofπ 1 of quasi projective manifolds, J. Alg. Geom., to appear.Google Scholar
  18. [JZ2]Jost, J. andZuo, K., Harmonic maps into Tits buildings and factorization of non rigid and non arithmetic representations ofπ 1 of algebraic varieties.Google Scholar
  19. [KS]Korevaar, N. andSchoen, R.,Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom.1 (1993), 561–569.MathSciNetGoogle Scholar
  20. [K]Kourouma, M.,Harmonic sections of Riemannian fiber bundles.Google Scholar
  21. [La]Labourie, F.,Existence d'applications harmoniques tordues à valeurs dans les variétés à courbure négative, Proc. AMS111 (1991), 877–882.CrossRefMathSciNetGoogle Scholar
  22. [N]Nikolaev, I.,Synthetic methods in Riemannian geometry, Lecture Notes.Google Scholar
  23. [Re]Reshetnyak, Y. G.,Nonexpanding maps in a space of curvature no greater than K, Siberian Math. Journ.9 (1968), 683–689.Google Scholar

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Fakultät und Institut für MathematikRuhr-Universität BochumBochum

Personalised recommendations