Minimizing fibrations and p-harmonic maps in homotopy classes from S3 into S2

Communications in Analysis and Geometry

Volumn 6, Issue 3, 1998, Pages 427-483

  Rivière, Tristan ^a  

^a CNRS   (France)

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[No Author keywords available]

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EID: 0347663712     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.1998.v6.n3.a2     Document Type: Article

References (23)

1. R. Bott and L. Tu, Differential forms in algebraic topology, GTM 82, Springer.
2. J.-M. Coron and R. D. Gulliver, Minimizing p-harmonic maps into spheres, J. reine angew. Math. 401 (1989), 82-100.
3. F. Duzaar and M. Fuchs, On removable singularities of p-harmonic maps, Ann. Inst. Henri Poincaré 7(5) (1990), 385-405.
4. F. Duzaar and E. Kuwert, Minimization of Conformally Invariant Energies in Homotopy Classes, to appear.
5. J. Eells and A. Ratto, Harmonic maps and minimal immersions with symmetries, Ann. of Math. Studies 130 Princeton University Press.
6. A. El Soufi, Indice de Morse des applications harmoniques de la sphère, Compo. Math. 95 (1995), 343-362.
7. A. M. Garsia and E.Rodemich, An embedding of Riemann surfaces of genus one, Pacific J. Math. 11 (1961), 193-204.
8. S. Gallot et D. Meyer, Operateur de courbure et Laplacien des formes différentielles d'une variété riemannienne, J. Math. Pures Appl. 54 (1975),259-299.
9. p-norm of the gradient, Comm. Pure App. Math. XL (1987), 555-588.
10. D. Husemoller, Fiber bundles, GTM 20, Springer.
11. n(ℂ), Osaka J. Math. 15(3) (1978), 515-546.
12. Y. Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer, (1992).
13. n, Proc. Japan Acad. 55, ser. A (1979), 141-145.
14. P. Li and S.T. Yau, A new conformal invariant and its applications to the Willmore conjecture and first eigenvalue of compact surfaces, Invent. Math. 69 (1982), 269-291.
15. P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Part I Rev. Math. Iberoamer. I 1 (1985), 145-200. Part II Rev. Math. Iberoamer. I 2 (1985), 45-121.
16. P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Part I Rev. Math. Iberoamer. I 1 (1985), 145-200. Part II Rev. Math. Iberoamer. I 2 (1985), 45-121.
17. S. Montiel and A. Ros, Minimal immersions of surfaces by the first eigenfunctions and conformal area, Invent. Math. 83 (1986), 153-166.
18. N. Nakauchi and S. Takakuwa, A remark on p-harmonic maps, Nonlinear Analysis 25(2) (1995).
19. 3, Invent. Math. 81 (1985), 379-386.
20. J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. Math. 113 (1981), 1-24.
21. R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Diff. Geom. 18 (1983), 253-268.
22. H. Urakawa, Stability of harmonic maps and eigenvalues of the Laplacian, Trans. Amer. Math. Soc. 301, 2 (1987), 557-589.
23. S.W. Wei and C.M. Yau, Regularity of p-energyminimizing map and p-superstrongly unstable indices, J. Geom. Anal. 4(2) (1994), 247-272.