p-minimising tangent maps and harmonic k-forms
Montaldo, Stefano
Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999), p. 331-339 / Harvested from Biblioteca Digitale Italiana di Matematica
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Si studiano le applicazioni p-tangenti da Rm a Sn date come estensioni omogenee di k-forme armoniche. Vengono ricavate condizioni necessarie sul grado k affinche tali applicazioni p-tangenti siano di energia minima. Una classificazione completa viene data nel caso in cui tali applicazioni tangenti di energia minima vadano da R8 su S4.

Publié le : 1999-06-01
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     author = {Stefano Montaldo},
     title = {$p$-minimising tangent maps and harmonic $k$-forms},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2-A},
     year = {1999},
     pages = {331-339},
     zbl = {0933.58019},
     mrnumber = {1706588},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2B_2_331_0}
}

Montaldo, Stefano. $p$-minimising tangent maps and harmonic $k$-forms. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 331-339. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2B_2_331_0/

[1] Baird, P., Harmonic Maps with Symmetry, Harmonic Morphisms, and Deformation of Metrics, Research Notes in Math., 87, Pitman, Boston, London, Melbourne (1983). | MR 716320 | Zbl 0515.58010

[2] Bairdand, P.-Ou, Y. L., Harmonic maps and morphisms from multilinear norm-preserving mappings, Internat. J. Math., to appear. | MR 1442435 | Zbl 0885.58013

[3] Coronand, J.-M.-Gulliver, R., Minimizing p-harmonic maps into spheres, J. Reine Angew. Math., 401 (1989), 82-100. | MR 1018054 | Zbl 0677.58021

[4] Eellsand, J.-Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc., 20 (1988), 385-524. | MR 956352 | Zbl 0669.58009

[5] Eellsand, J.-Ratto, A., Harmonic Maps and Minimal Immersions with Symmetries, Ann. Math. Stud., 130, Princeton University Press (1993). | MR 1242555 | Zbl 0783.58003

[6] Gauchmanand, H.-Toth, G., Constructions of harmonic polynomial maps between spheres, Geom. Dedicata, 50 (1994), 57-79. | MR 1280796 | Zbl 0805.58020

[7] Hardt, R.-Lin, F.H., Mappings minimizing the Lp-norm of the gradient, Comm. Pure Appl. Math., 40 (1987), 555-588. | MR 896767 | Zbl 0646.49007

[8] Montaldo, S., Stability of harmonic maps and morphisms, Thesis, Leeds University (1996).

[9] Nakauchi, N., Regularity of minimizing p-harmonic maps into the sphere, Boll. Un. Mat. Ital., 10-A (1996), 143-156. | MR 1386252 | Zbl 0849.58021

[10] Nash, J. F., The imbedding problem for Riemannian manifolds, Ann. Math., 63 (1956), 20-63. | MR 75639 | Zbl 0070.38603

[11] Parker, M., Orthogonal multiplications in small dimensions, Bull. London Math. Soc., 15 (1983), 368-372. | MR 703763 | Zbl 0494.58017

[12] Schoen, R.-Uhlenbeck, K., A regularity theory for harmonic maps, J. Diff. Geom., 17 (1982), 307-335. | MR 664498 | Zbl 0521.58021

[13] Schoen, R.-Uhlenbeck, K., Regularity of minimizing harmonic maps into the sphere, Invent. Math., 78 (1984), 89-100. | MR 762354 | Zbl 0555.58011

[14] Wood, R., Polynomial maps from spheres to spheres, Invent. Math., 5 (1968) 163-168. | MR 227999 | Zbl 0204.23805

[15] Yiu, P., Quadratic forms between spheres and the non-existence of sums of squares formulae, Math. Proc. Cambridge Philos. Soc., 100 (1986), 493-504. | MR 857724 | Zbl 0613.55009