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Hitchin's self-duality equations on complete Riemannian manifolds

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References

  • [A-S] Anderson, M.T., Schoen, R.: Positive harmonic functions on complete manifolds of negative curvature. Ann. Math.121, (1985), 429–461

    Google Scholar 

  • [Ch] Cheng, S.Y.: Liouville theorem for harmonic maps. Proc. Sympos. Pure Math.36 (1980), 147–151

    Google Scholar 

  • [C1] Corlette, K.: FlatG-bundles with canonical metrics. J. Diff. Geom.28 (1988), 361–382

    Google Scholar 

  • [C2] Corlette, K.: Archimedean superrigidity and hyperbolic geometry. Ann. Math.135 (1992), 165–182

    Google Scholar 

  • [D-W] Ding, W.-Y., Wang, Y.: Harmonic maps of complete noncompact Riemannian manifolds. Intern. J. Math.2 (1991), 617–633

    Google Scholar 

  • [D1] Donaldson, S.K.: Twisted harmonic maps and the self-duality equations. Proc. London Math. Soc.55 (1987), 127–131

    Google Scholar 

  • [D2] Donaldson, S.K.: Boundary value problems for Yang-Mills fields. J. Geom. Phys.8 (1992), 89–122

    Google Scholar 

  • [Do] Donnelly, H.: On the essential spectrum of a complete Riemannian manifold. Topology20 (1981), 1–14

    Google Scholar 

  • [G-T] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Springer-Verlag, 1977

  • [H] Hamilton, R.: Harmonic maps of manifolds with boundary. Lect. Notes in Math. 471. Springer-Verlag, Berlin, 1975

    Google Scholar 

  • [Hi] Hitchin, N.J.: The self-duality equations on a Riemann surface Proc. London Math. Soc.55 (1987), 59–126

    Google Scholar 

  • [J-Z] Jost, J., Zuo, K.: Harmonic maps andSl(r, ℂ)-representations of π1 of quasi projective manifolds. Preprint

  • [L] Li, J.: The heat flows and harmonic maps of complete noncompact Riemannian manifolds. Math. Z.212 (1993), 161–173

    Google Scholar 

  • [Lo] Lohkamp, J.: An existence theorem for harmonic maps. Manu. Math.67 (1990), 21–23

    Google Scholar 

  • [Mo] Moser, J.: On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math.14 (1961), 577–591

    Google Scholar 

  • [N-S] Narasimhan, M.S., Seshadri, C.S.: Stable and unitary vector bundles on a compact Riemann surface. Ann. Math.82, (1965), 540–567

    Google Scholar 

  • [S-Y] Schoen, R., Yau, S.T.: Compact group actions and the topology of manifolds with nonpositive curvature. Topology18 (1979), 361–380

    Google Scholar 

  • [S] Simpson, C.T.: Harmonic bundles on noncompact curves. J. Amer. Math. Soc.3 (1990), 713–770

    Google Scholar 

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Jiayu, L. Hitchin's self-duality equations on complete Riemannian manifolds. Math. Ann. 306, 419–428 (1996). https://doi.org/10.1007/BF01445258

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