Geodesic
Harmonic Mappings of Negatively Curved Manifolds
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 631-637

Voir la notice de l'article provenant de la source Cambridge University Press

Volume decreasing properties of harmonic mappings of space forms were investigated by S. S. Chern and S. I. Goldberg [3] and the author. In a previous paper [6], a step toward generalization of the results was made proving the following theorem:Theorem. Let ƒ: M —> N be a harmonic mapping of n-dimensional Riemannian manifolds, with C ≦ 0. Suppose the scalar curvature of M is not less than — S, and the Ricci curvature of N is not greater than —S/n, where S ≧ 0 and S > 0 are constants. Then, if u has a maximum on M, i.e. ƒ is volume decreasing up to a constant. 
Har'el, Zvi. Harmonic Mappings of Negatively Curved Manifolds. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 631-637. doi: 10.4153/CJM-1978-054-4
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