On the Generalized of p-harmonic Maps

Year 2022, Volume: 15 Issue: 2, 183 - 191, 31.10.2022

Bouchra Merdji Ahmed Mohammed Cherif

https://doi.org/10.36890/iejg.1085856

Abstract

In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds.
We present some new properties for the generalized stable p-harmonic maps.

Keywords

$p$-harmonic maps, $p$-biharmonic maps, stable $p$-harmonic maps

References

• [1] Baird, P., Wood, J. C.: Harmonic morphisms between Riemannain manifolds. Clarendon Press, Oxford (2003).
• [2] Baird, P., Gudmundsson, S.: p-Harmonic maps and minimal submanifolds. Math. Ann. 294, 611-624 (1992).
• [3] Bojarski, B., Iwaniec, T.: p-Harmonic equation and quasiregular mappings. Banach Center Publ. 19 (1), 25-38 (1987).
• [4] Cheung, L-F., Leung, P-F.: Some results on stable p-harmonic maps. Glasgow Math. J. 36, 77-80 (1994).
• [5] Eells, J., Sampson, J. H.:Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109-160 (1964).
• [6] Fardoun, A.: On equivariant p-harmonic maps. Ann. Inst. Henri. Poincare. 15, 25-72 (1998).
• [7] Jiang, G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7 (4), 389-402 (1986).
• [8] Mohammed Cherif, A.: On the p-harmonic and p-biharmonic maps. J. Geom. 109 (41), (2018).
• [9] Nagano, T., Sumi M.: Stability of p-harmonic maps. Tokyo J. Math. 15 (2), 475-482 (1992).
• [10] Xin Y.: Geometry of harmonic maps. Fudan University (1996).