On p-harmonic morphisms

Differential Geometry and its Application

Volumn 12, Issue 3, 2000, Pages 219-229

  Loubeau, E ^a  

^a UFR SCIENCES ET TECHNIQUES   (France)

Author keywords

P harmonic maps; P harmonic morphisms

Indexed keywords

EID: 0034179456     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(00)00013-9     Document Type: Article

References (21)

1. S. Alinhac and P. Gerard, OpéRateurs Pseudo-différentiels et Théorème de Nash-moser (Savoirs Actuels. InterEditions, Editions du CNRS, Paris, 1991).
2. P. Baird and J. Eells, A conservation law for harmonic maps, in: E. Looijenga, D. Siersma and F. Takens, eds., Geometry Symposium. Utrecht 1980, Lecture Notes in Math. 894 (Springer, Berlin, 1981) 1-25.
3. P. Baird and J. Eells, A conservation law for harmonic maps, in: E. Looijenga, D. Siersma and F. Takens,eds., Geometry Symposium. Utrecht 1980, Lecture Notes in Math. 894 (Springer, Berlin, 1981) 1-25.
4. P. Baird and S. Gudmundsson, p-harmonic maps and minimal submanifolds, Math. Ann. 294 (1992) 611-624.
5. A. Bernard, E.A. Campbell and A.M. Davie, Brownian motion and generalized analytic and inner functions, Ann. Inst. Fourier (Grenoble) 29 (1979) 207-228.
6. R.W.R. Darling, Martingales in manifolds. Definition, examples and behaviour under maps, in: J. Azéma and M. Yor, eds., Séminaire de probabilités XVI 1980/91 supplément: géométrie différentielle stochastique, Lecture Notes in Math. 921 (Springer, Berlin, 1982) 217-236.
7. F. Duzaar and M. Fuchs, Existence and regularity of functions which minimize certain energies in homotopy classes of mappings, Asymptotic Anal. 5 (1991) 129-144.
8. J. Eells, p-harmonic and Exponentially Harmonic Maps, lecture given at Leeds University, June 1993.
9. J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conf. Ser. in Math. 50 (Amer. Math. Soc., Providence, 1983).
10. J. Eells and J.H. Sampson, Harmonic mappings of riemannian manifoids, Amer. J. Math. 86 (1964) 109-160.
11. B. Fuglede, Harmonic morphisms between riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978) 107-144.
12. B. Fuglede, Harmonic morphisms between semi-riemannian manifolds, Ann. Acad. Sci. Fenn. Ser. A I Math. 21 (1996) 31-50.
13. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, A Series of ComPrehensive Studies in Mathematics 224 (Springer, Berlin, 1977).
14. p -norm of the gradient, Comm. Pure Appl. Math. 40 (1987) 555-588.
15. T. Ishihara, A mapping of riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979) 215-22.
16. C.G. Jacobi, Über eine lösung der partiellen differentialgleichung δ(v) = 0, J. Reine Angew. Math. 36 (1848) 113-134.
17. P. Lévy, Processus Stochastique et Mouvements Brownien (Gauthier-Villars, Paris, 1948).
18. S. Luckhaus, Partial hölder continuity for energy minimizing p-harmonic maps between riemannian manifolds, Indiana Univ. Math. J. 37 (1988) 349-367.
19. H. Takeuchi, Stability and liouville theorems of p-harmonic maps, Japan J. Math. (n.S.) 17 (1991) 317-332.
20. H. Takeuchi, Some conformal properties of p-harmonic maps and regularity for sphere-valued p-harmonic maps, J. Math. Soc. Japan 46 (1994) 217-234.
21. K. Uhlenbeck, Harmonic maps: A direct method in the calculus of variations, Bull. Amer. Math. Soc. 76 (1970) 1082-1987.