Harmonic gauges on Riemann surfaces and stable bundles

Giogio Valli

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 3, page 233-245
  • ISSN: 0294-1449

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Valli, Giogio. "Harmonic gauges on Riemann surfaces and stable bundles." Annales de l'I.H.P. Analyse non linéaire 6.3 (1989): 233-245. <http://eudml.org/doc/78176>.

@article{Valli1989,
author = {Valli, Giogio},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {harmonic map; Uhlenbeck loop; semistable vector bundle},
language = {eng},
number = {3},
pages = {233-245},
publisher = {Gauthier-Villars},
title = {Harmonic gauges on Riemann surfaces and stable bundles},
url = {http://eudml.org/doc/78176},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Valli, Giogio
TI - Harmonic gauges on Riemann surfaces and stable bundles
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 3
SP - 233
EP - 245
LA - eng
KW - harmonic map; Uhlenbeck loop; semistable vector bundle
UR - http://eudml.org/doc/78176
ER -

References

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  1. [A-B] M.F. Atiyah and R. Bott, The Yang-Mills Equations over Riemann Surfaces, Phil. Trans. R. Soc. London, Vol. A308, pp. 523-615. Zbl0509.14014MR702806
  2. [B-R 1] F. Burstall and J. Rawnsley, Sphères harmoniques, etc., C.R. Acad. Sci. Paris, T. 302, Series I, 1986, pp. 709-712. Zbl0594.58024MR850325
  3. [B-R 2] F. Burstall and J. Rawnsley, Twistors, Harmonic Maps, and Homogeneous Geometry (in preparation). 
  4. [D 1] S.K. Donaldson, A New Proof of a Theorem of Narasimhan and Seshadri, J. Diff. Geometry, Vol. 18, 1983, pp. 269-277. Zbl0504.49027MR710055
  5. [D2] S.K. Donaldson, Anti-Self-Dual Yang-Mills Connections over Complex Algebraic Surfaces and Stable Vector Bundles, Proc. London Math. Soc., Vol. 50, 1985, pp. 1-26. Zbl0529.53018MR765366
  6. [G] B. Gaveau, Intégrales harmoniques non-abéliennes, Bull. Sc. Math., 2e série, T. 106, 1982, pp. 113-169. Zbl0569.58002MR666740
  7. [H 1] N. Hitchin, Harmonic Maps from a 2-Torus to the 3-Sphere, Preprint, 1987. MR1053342
  8. [H 2] N. Hitchin, Self-Duality Equations on a Riemann Surface, Proc. London Math. Soc., Vol. 55, 1987, pp. 59-126. Zbl0634.53045MR887284
  9. [H 3] N. Hitchin, Stable Bundles and Integrable Systems, Duke Math. J., Vol. 54, 1987, pp. 91-114. Zbl0627.14024MR885778
  10. [O] Y. Ohnita, On Pluriharmonicity of Stable Harmonic Maps, J. London Math. Soc., Vol. 35, 1987, pp. 563-568. Zbl0588.58019MR889377
  11. [O-V] Y. Ohnita and G. Valli, Pluriharmonic Maps into Lie Groups, Max-Plank-Institut, preprint, 1989. 
  12. [U] K. Uhlenbeck, Harmonic Maps into Lie Groups (Classical Solutions of the Chiral Model), Preprint, University of Chicago, 1985. Zbl0677.58020MR1001271
  13. [V1] G. Valli, On the Energy Spectrum of Harmonic 2-Spheres in Unitary Groups. Topology (to appear). Zbl0744.53027MR948176
  14. [V2] G. Valli, Some Remarks on Geodesics in Gauge Groups and Harmonic Maps, Preprint, International Centre of Theoretical Physics, Trieste, 1987. Zbl0656.58010MR957018
  15. [V3] G. Valli, Ph.D. Thesis, University of Warwick (G. B.) (in preparation). 
  16. [W] J.C. Wood, Explicit Construction and Parametrization of Harmonic 2-Spheres in the Unitary Group, Preprint, University of Leeds, 1987. 

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