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Harmonic Mappings of Negatively Curved Manifolds
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1978
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